21. Motivic Homotopy Theory - Algebraic Topology Journals, Books & Online Media | Sp Motivic Homotopy Theory Geometry topology. grothendieck topologies; Model categories; Motivic spaces and spectra; Nisnevich topology http://www.springer.com/978-3-540-45895-1

Please select Africa Asia Australia / Oceania Europe France Germany Italy North America South America Switzerland United Kingdom All Author/Editor Title ISBN/ISSN Series Journals Series Textbooks Contact Select your subdiscipline Algebra Analysis Applications Mathematical Biology Mathematical Physics Probability Theory Quantitative Finance Select a discipline Astronomy Biomedical Sciences Chemistry Computer Science Economics Education Engineering Environmental Sciences Geography Geosciences Humanities Law Life Sciences Linguistics Materials Mathematics Medicine Philosophy Physics Psychology Public Health Social Sciences Statistics Home Mathematics Motivic Homotopy Theory Lectures at a Summer School in Nordfjordeid, Norway, August 2002 Series: Universitext Dundas , B.I., Levine , M., ˜stv¦r , P.A., R¶ndigs , O., Voevodsky , V. 2007, X, 226 p., Softcover ISBN: 978-3-540-45895-1 This item usually ships in 2-3 business days. About this textbook Table of contents About this textbook This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.

22. Seminar On Cohomology Goal grothendieck topologies and etale and crystalline cohomologies; applications to zeta functions and the Weil conjectures; de Rham cohomology and its http://www.math.mcgill.ca/goren/SeminarOnCohomology.html

Seminar on Cohomology Theories Schedule: September 17 Gabriel Chenevert and Payman Kassaei Review of homological algebra, sheaf cohomology via derived functors and via Cech cohomology, some key theorems, examples of cohomology groups (in particular, Zariski is no good for constant coefficients). September 24 Gabriel Chenevert and Payman Kassaei Continued. notes Andrew Archibald and Alex Ghitza Grothendieck topologies. The etale topology: flat and unramified morphisms. Etale morphisms and criteria. Lots of examples. Sheaves in the etale topology. The stalk of a sheaf. October 1 Andrew Archibald and Alex Ghitza Continued. October 8 Andrew Archibald and Alex Ghitza Continued notes October 10 Elena Mantovan (BURN 1205, 10:30-11:00 and 1:30-2:30) The role of the geometry of Shimura varieties in the Langlands' conjectures October 15 Eyal Goren; Gil Alon Some remarks on etale morphism; Descent and a Grothendieck topology. October 22 Gil Alon Descent and a Grothendieck topology (Cont'd). notes October 29 Pete Clark and Marc-Hubert Nicole de Rham cohomology and the Hodge to de Rham spectral sequence. Algebraic de Rham cohomology. The crystalline topology. Divided powers. The crystalline site. Lots of examples.

23. [cs/0512008] Cohomology In Grothendieck Topologies And Lower Bounds In Boolean C We describe an approach to attacking such questions with cohomology, and we show that using grothendieck topologies and other ideas from the grothendieck http://arxiv.org/abs/cs.CC/0512008

arXiv.org cs Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PostScript PDF Other formats Citations CiteBase cs new recent Computer Science > Computational Complexity Title: Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity Authors: Joel Friedman (Submitted on 1 Dec 2005 ( ), last revised 2 Dec 2005 (this version, v2)) Abstract: This paper is motivated by questions such as P vs. NP and other questions in Boolean complexity theory. We describe an approach to attacking such questions with cohomology, and we show that using Grothendieck topologies and other ideas from the Grothendieck school gives new hope for such an attack. We focus on circuit depth complexity, and consider only finite topological spaces or Grothendieck topologies based on finite categories; as such, we do not use algebraic geometry or manifolds. Given two sheaves on a Grothendieck topology, their "cohomological complexity" is the sum of the dimensions of their Ext groups. We seek to model the depth complexity of Boolean functions by the cohomological complexity of sheaves on a Grothendieck topology. We propose that the logical AND of two Boolean functions will have its corresponding cohomological complexity bounded in terms of those of the two functions using ``virtual zero extensions.'' We propose that the logical negation of a function will have its corresponding cohomological complexity equal to that of the original function using duality theory. We explain these approaches and show that they are stable under pullbacks and base change. It is the subject of ongoing work to achieve AND and negation bounds simultaneously in a way that yields an interesting depth lower bound.

24. Grothendieck Topologies And Deformation Theory II Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.springerlink.com/index/H053WX02557272G5.pdf

25. Citebase - Grothendieck Topologies And Ideal Closure Operations Notes on grothendieck topologies, fibered categories and descent theory. In B. Fantechi, L. Göttsche, L. Illusie, S. Kleiman, N. Nitsure, A. Vistoli, http://www.citebase.org/abstract?identifier=oai:arXiv.org:math/0612471&action=ci

26. PlanetMath: Site 18F10 (Category theory; homological algebra Categories and geometry grothendieck topologies). 18F20 (Category theory; homological algebra http://planetmath.org/encyclopedia/Covering.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About site (Definition) Definition A site is a generalization of a topology , designed to address the problem that in the algebraic category , the only reasonable topology is the Zariski topology , in which the open sets are much too large. In order to obtain a well-behaved cohomology theory (and an algebraic version of the fundamental group Using the machinery of sites, one can construct (or -adic) cohomology, and one can construct crystalline cohomology, both of which can be used to prove the Weil conjectures , and both of which serve as generalizations of the familiar cohomology from topology and complex analysis Fix a universe Definition A site is a -category whose objects of collections of maps of is a small set of morphisms in . These objects must satisfy the following: If is an isomorphism , then is a covering.

27. JSTOR The Cohomological Dimension Of Certain Grothendieck Topologies The cohomological dimension of certain grothendieck topologies By Stephen S. Shatz* Introduction We study the cohomology and structure of the category of http://links.jstor.org/sici?sici=0003-486X(196605)2:83:3<572:TCDOCG>2.0.CO;2-G

28. ResearchChannel - Cohomology In Grothendieck Topologies And Lower We shall show that if one generalizes the setting to grothendieck topologies, it may be possible to circumvent two obstacles to connecting Boolean depth http://www.researchchannel.org/prog/displayevent.aspx?rID=4863

29. ALGEBRAIC TOPOLOGY OF ALGEBRAIC VARIETIES Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.turpion.org/php/full/infoFT.phtml?journal_id=rm&paper_id=1192&year_id

30. Alexander Schmidt: Coarse Geometry Via Grothendieck Topologies Titel Coarse geometry via grothendieck topologies Jahr 1997 In Math. Nachr. 203 (1999), 159173. Preprint dvi-file grob.dvi http://www.mathematik.uni-regensburg.de/Schmidt/papers/schmidt07-de.html

Alexander Schmidt: Coarse geometry via Grothendieck topologies Autor: Alexander Schmidt Titel: Coarse geometry via Grothendieck topologies Jahr: In: Math. Nachr. 203 (1999), 159-173 Preprint dvi-file grob.dvi

31. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection grothendieck topologies 18F10 grothendieck topologies and cohomologies \ etale and other 14F20 ground fields arithmetic 14H25 http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_25.htm

geometry # general aspects of Euclidean geometry # geometric orders, order geometry # global differential geometry # incidence geometry # integral geometry # line geometry # linear incidence geometry # local analytic geometry # local differential geometry # local Riemannian geometry # methods of noncommutative geometry # methods of Riemannian geometry # metric geometry # Minkowski geometry # modern geometry # modular geometry # non-Euclidean differential geometry # noncommutative geometry # noncommutative algebraic geometry # noncommutative differential geometry # nonlinear incidence geometry # numerical methods in geometry # other complex differential geometry # plane geometry # plane analytic geometry # projective geometry # projective analytic geometry # projective and enumerative geometry # projective differential geometry # questions of classical algebraic geometry # random convex sets and integral geometry # real algebraic and real analytic geometry # real and complex geometry # relations with differential geometry # Riemannian geometry # rigid analytic geometry # rings arising from non-commutative algebraic geometry # solid geometry # solid analytic geometry # spin and Spin$^c$ geometry # sub-Riemannian geometry # symplectic geometry, contact

32. ScienceDirect - Journal Of Algebra : The Primitive Topology Of A Scheme*1, *2 Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://linkinghub.elsevier.com/retrieve/pii/S0021869397972896

Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page Journal of Algebra Volume 201, Issue 2 , 15 March 1998, Pages 656-685 Abstract Abstract + References PDF (305 K) Related Articles in ScienceDirect Local and global solutions of a differential equation o... Indagationes Mathematicae (Proceedings) Local and global solutions of a differential equation on a curve Indagationes Mathematicae (Proceedings) Volume 89, Issue 1 Pages 99-104 M. van der Put Abstract Abstract + References PDF (309 K) View More Related Articles ... doi:10.1006/jabr.1997.7289 Regular Article The Primitive Topology of a Scheme Mark E. Walker Abstract We define a Grothendieck topology on the category of schemes whose associated sheaf theory coincides in many cases with that of the Zariski topology. We also give some indications of possible advantages this new topology has over the Zariski topology. Author Keywords: K -theory; local-global ring; primitive criterion; pretheory

33. Bibliografia Chapter III takes up grothendieck topologies, sheaves on a site, and the category of the latter. There is an illuminating discussion of how an effort to http://www.disi.unige.it/person/RosoliniG/ILM/bib01.html

Testi di riferimento con recensioni e collocazione presso il CSBMI ed altri CSB Barr, Michael; Wells, Charles Category theory for computing science. Prentice Hall International Series in Computer Science. Prentice Hall International, New York, ISBN Collocazione MAT 68-1995-095, MAT 18-1990-08 The present volume contains an exposition of some of the central topics of category theory, adapted mainly to the interests of researchers and students in computing science. The appearance of a book of this kind is now fully motivated by the increasing use of categorical ideas and constructions in computing science, in particular in the modeling of linguistic and computational phenomena. One important feature of this work is the systematic use by the authors of C. Ehresmann's concept of a sketch as a formal abstract specification of a mathematical structure. Each section of the text contains a set of exercises that complement the exposition by providing further examples and results. Detailed solutions to all the exercises are collected in a large appendix following the main text. The authors have succeeded in producing a book which is original in its contents and exposition, and accessible to a broad public of readers. People specializing in theoretical computing science will find here a solid category-theoretic foundation; while those interested mainly in category and topos theory could use it as an introduction to the authors' earlier, more specialized monograph [Toposes, triples and theories, Springer, New York, 1985; MR 86f:18001].

34. List KWIC DDC And MSC Lexical Connection grothendieck topologies 18F10 grothendieck topologies and cohomologies etale and other 14F20 ground fields arithmetic 14H25 http://www.mi.imati.cnr.it/~alberto/dml_11_22.htm

graphs and maps # chromatic theory of graphs and maps # enumeration of graphs and matrices graphs and networks # boundary value problems on graphs or networks # programming involving graphs, bandwidth, etc.) # graph labelling (graceful graphs, diagram schemes, precategories graphs; applications of algebraic topology and algebraic geometry # Feynman integrals and Grassmannians, Schubert varieties, flag manifolds Grassmannians, Veronesians and their generalizations) # synthetic treatment of fundamental manifolds in projective geometries ( gravitational energy and conservation laws; groups of motions gravitational field # quantization of the gravitational field with matter (hydrodynamics, etc.) # macroscopic interaction of the gravitational interaction gravitational theories other than Einstein's, including asymmetric field theories # relativistic gravitational theory # relativity and 83-XX gravitational waves gravity # density and specific gravity # mass and gravity of solids; projectiles # mass and gravity, Regge calculus and other discrete methods # lattice

35. Book Categories Sheaves, (comprehensive Studies In Mathematics Series, Vol. 332) Unbounded Derived Categories. Indization and Derivation of Abelian Categories.- grothendieck Topologies.- Sheaves on grothendieck Topologies. http://www.lavoisier.fr/notice/gb411683.html

Search on All Book CD-Rom eBook Software The french leading professional bookseller Description Approximate price Author(s) : KASHIWARA Masaki, SCHAPIRA Pierre Publication date : 09-2005 Language : ENGLISH Status : In Print (Delivery time : 10 days) Description Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays. This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies. Summary The language of categories.- Limits.- Filtrant Limits.- Tensor categories.- Generators and Representability.- Indization of categories.- Localization.- Additive and Abelian categories.- pi-accessible objects and F-injective Objects.- Triangulated Categories.- Complexes in additive categories.- Complexes in Abelian Categories.- Derived Categories.- Unbounded Derived Categories.- Indization and Derivation of Abelian Categories.- Grothendieck Topologies.- Sheaves on Grothendieck Topologies.- Abelian Sheaves.- Stacks and Twisted Sheaves.- References.- Notations.

36. Ars Mathematica » 2006 » July Wikipedia on grothendieck topologies and topos theory Check out their dry but complete summary of grothendieck topologies, and their more evocative http://www.arsmathematica.net/archives/2006/07/page/2/

Ars Mathematica Dedicated to the mathematical arts. Archive for July, 2006 Baez Week 235 Saturday, July 15th, 2006 Week 235 Posted in Physics Mathematics More on Grothendieck topologies Thursday, July 13th, 2006 schemes and representable functors , you can find a nice introduction to Grothendieck topologies here: Notes on Grothendieck topologies, fibered categories and descent theory , by Angelo Vistoli. Posted in Mathematics Extra Dimensions in Physics Sunday, July 9th, 2006 Bee at Backreaction has written the definitive weblog post on the experimental search for evidence of the existence of extra dimensions Posted in Physics Freese on Universal Algebra Saturday, July 8th, 2006 A few universal algebra links , collected by Ralph Freese Universal algebra isomorphism theorems Posted in Mathematics Wikipedia on Grothendieck topologies and topos theory Wednesday, July 5th, 2006 Grothendieck topologies , and their more evocative Background and genesis of topos theory Posted in Mathematics Big Bang Bad? Sunday, July 2nd, 2006 Rob Knop thinks that the Big Bang is a bad name for a good theory. Read this post primordial atom Posted in Physics July 2006 M T W T F S S Recent Posts Representative from Fermilab Cauchy-Schwartz Theorem Your Weakness, Revealed

37. DBLP: Joel Friedman 36 EE, Joel Friedman Cohomology in grothendieck Topologies and Lower Bounds in Boolean Complexity II A Simple Example CoRR abs/cs/0604024 (2006) http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/f/Friedman:Joel.html

Joel Friedman List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... EE Joel Friedman: Linear Transformations in Boolean Complexity Theory. CiE 2007 EE Robert St-Aubin , Joel Friedman, Alan K. Mackworth : A formal mathematical framework for modeling probabilistic hybrid systems. Ann. Math. Artif. Intell. 47 EE Joel Friedman: Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity II: A Simple Example CoRR abs/cs/0604024 EE Joel Friedman, Ram Murty Jean-Pierre Tillich : Spectral estimates for Abelian Cayley graphs. J. Comb. Theory, Ser. B 96 EE Joel Friedman: Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity CoRR abs/cs/0512008 EE Joel Friedman, Andreas Goerdt Michael Krivelevich : Recognizing More Unsatisfiable Random k-SAT Instances Efficiently. SIAM J. Comput. 35 EE Joel Friedman, Jean-Pierre Tillich : Generalized AlonBoppana Theorems and Error-Correcting Codes. SIAM J. Discrete Math. 19 EE Joel Friedman: A proof of Alon's second eigenvalue conjecture and related problems CoRR cs.DM/0405020

38. Front: Author D.Gaitsgory alggeom/9508004 grothendieck topologies and deformation theory II. alg-geom/9502010 Operads, grothendieck topologies and Deformation theory. http://front.math.ucdavis.edu/author/D.Gaitsgory

Front for the arXiv Fri, 14 Mar 2008 Front author search register submit journals ... iFAQ Articles by D.Gaitsgory Articles to of arXiv:0712.0788 D-modules on the affine flag variety and representations of affine Kac-Moody algebras. Edward Frenkel , Dennis Gaitsgory math.RT math.AG arXiv:0711.1132 Local Geometric Langlands Correspondence: the Spherical Case. Edward Frenkel , Dennis Gaitsgory math.QA math.AG math.RT ... arXiv:0706.3725 Weyl modules and opers without monodromy. Edward Frenkel , Dennis Gaitsgory math.QA math.AG math.RT ... arXiv:0705.4571 Twisted Whittaker model and factorizable sheaves. Dennis Gaitsgory math.RT math.QA math/0611323 Spherical varieties and Langlands duality. D. Gaitsgory , D. Nadler math.RT math.AG math/0605139 Deformations of local systems and Eisenstein series. A. Braverman , D. Gaitsgory math.AG math.RT math.RT/0603524 Geometric realizations of Wakimoto modules at the critical level. E. Frenkel , D. Gaitsgory math.RT math.AG math.RT/0512562 Localization of g^-modules on the affine Grassmannian. Edward Frenkel , Dennis Gaitsgory math.RT math.AG math.QA ... math/0511284 Fusion and convolution: applications to affine Kac-Moody algebras at the critical level. Edward Frenkel , Dennis Gaitsgory math.RT

39. Algebraic Geometry Seminar 2006 Title Algebraic Geometry Seminar Cohomology in grothendieck Topologies and Lower Bounds in Boolean Complexity - Part II http://www.pims.math.ca/seminars.php?ps=list&event_type=Algebraic Geometry Semin

40. Gaitsgory - Author Index All Archive(s) Operads, grothendieck topologies and Deformation theory. D. Gaitsgory. Abstract Full text References Citations alggeom/9502010 (February 1995) http://eprintweb.org/S/authors/All/ga/Gaitsgory

Username: Password: Main Archive Authors Personalization ... GZ D. Gaitsgory Article(s): Archive: All Author Surname: Gaitsgory D-modules on the affine flag variety and representations of affine Kac-Moody algebras Edward Frenkel and Dennis Gaitsgory Abstract Full text References Citations arXiv:0712.0788 (December 2007) Weyl modules and opers without monodromy Edward Frenkel and Dennis Gaitsgory Abstract Full text References Citations arXiv:0706.3725 (June 2007) Twisted Whittaker model and factorizable sheaves Dennis Gaitsgory Abstract Full text References Citations arXiv:0705.4571 (May 2007) Spherical varieties and Langlands duality D. Gaitsgory and D. Nadler Abstract Full text References Citations math/0611323 (November 2006) Deformations of local systems and Eisenstein series A. Braverman and D. Gaitsgory Abstract Full text References Citations math/0605139 (May 2006) Geometric realizations of Wakimoto modules at the critical level E. Frenkel and D. Gaitsgory Abstract Full text References Citations math/0603524 (March 2006) Localization of g^-modules on the affine Grassmannian Edward Frenkel and Dennis Gaitsgory Abstract Full text References Citations math/0512562 (December 2005) Fusion and convolution: applications to affine Kac-Moody algebras at the critical level Edward Frenkel and Dennis Gaitsgory Abstract Full text References Citations math/0511284 (November 2005) Local geometric Langlands correspondence and affine Kac-Moody algebras Edward Frenkel and Dennis Gaitsgory Abstract Full text References Citations math/0508382 (August 2005) The notion of category over an algebraic stack

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