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Sunday, May 3, 2020 | History

1 edition of Generalized Etale Cohomology Theories found in the catalog.

Generalized Etale Cohomology Theories

John F. Jardine

# Generalized Etale Cohomology Theories

## by John F. Jardine

Written in English

Subjects:
• Mathematics,
• Algebraic Geometry,
• Homology theory

A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason"s descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for th.

Edition Notes

Description based on print version record.

Classifications The Physical Object Series Modern Birkha user Classics, Modern Birkha user classics LC Classifications QA564 .J34 2010 Format [electronic resource] Pagination 1 online resource (322 pages). Number of Pages 322 Open Library OL25537546M ISBN 10 3034800665 ISBN 10 9783034800662 OCLC/WorldCa 851971803

N etal: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in .

X n (Y) = [Y, X] −n = [S −n Y, X] is the generalized cohomology of Y Ordinary homology theories [ edit ] These are the theories satisfying the "dimension axiom" of the Eilenberg–Steenrod axioms that the homology of a point vanishes in dimension other than 0. A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a Author: Rick Jardine.

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer .   A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the .

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### Generalized Etale Cohomology Theories by John F. Jardine Download PDF EPUB FB2

A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem 5/5(1).

A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory.

This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem Brand: Birkhäuser Basel.

A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for Generalized Etale Cohomology Theories book.

Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces.

Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and. Etale cohomology is an important branch in arithmetic geometry.

This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology.

Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology.

A generalized étale cohomology theory is a graded group \(H*(T,F)\) (T,F), which is associated to a presheaf of spectra F on an étale site for a scheme T Keywords Cohomology Theory Weak Equivalence Homotopy Category Stable Homotopy Group Abelian SheafCited by: 3.

Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology.

The if-theory presheaf of spectra and its deloopings Products The algebraic if-theory product ^er Join transformations Chapter 6. Generalized etale cohomology The descent spectral sequence The classifying topos Ordinary Galois cohomology Generalized Cech. Jardine is Canada Research Chair and Professor of Mathematics at the University of Western Ontario.

He is the author of Generalized Etale Cohomology Theories and Simplicial Homotopy Theory Brand: Springer-Verlag New York. These theories come under the common name of generalized homology (or cohomology) theories.

The purpose of the book is to give an exposition of generalized (co)homology theories that can be read by a wide group of mathematicians who are not experts in algebraic topology. It starts with basic notions of homotopy theory and then introduces the.

\$\begingroup\$ Ali, I don't think there is a "Royal Road" to etale cohomology. If you have easy access to SGAtry it out. Maybe use it in conjunction with Milne's notes (and/or book) for things you don't understand.

If you can get access to one of the other books, even better. Why choose just one. \$\endgroup\$ – B R Nov 10 '11 at This means that from a perspective of higher category theory, generalized Eilenberg-Steenrod cohomology is the intrinsic cohomology of the (∞,1)-category of spectra, or better: twisted generalized Eilenberg-Steenrod cohomology is the intrinsic cohomology of the tangent (∞,1)-topos of parameterized spectra.

A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a This book is suitable for researchers working in fields related to algebraic K-theory.

14 results for Books: "etale cohomology" Skip to main search results Amazon Prime. Eligible for Free Shipping. Generalized Etale Cohomology Theories (Progress in Mathematics) by J.F. Jardine | Feb 4, Hardcover \$ \$ 55 \$ \$ \$ shipping. Princeton Mathematical Ser Princeton University Press, +xiii pages, ISBN An exposition of étale cohomology assuming only a knowledge of basic scheme theory.

In print. List price USD ( price was \$=\$ in dollars). etale A-theory is a (twisted) generalized cohomology theory on the etale homotopy type of Spec A, a theory which bears the same relationship to etale cohomology as the complex topological A-theory of spaces does to singular cohomology.

From a pragmatic point of view, the main achievement of etale A-theory is to manufacture. Then the authors discuss various types of generalized cohomology theories, such as complex-oriented cohomology theories and Chern classes, \(K\)-theory, complex cobordisms, and formal group laws.

A separate chapter is devoted to spectral sequences and their use in generalized cohomology theories. The book is intended to serve as an introduction.

A generalized cohomology theory is a pair, where is a functor from the category of pairs of topological spaces into the category of graded Abelian groups (that is, to each pair of spaces corresponds a graded Abelian group and to each continuous mapping a set of homomorphisms), and is a set of homomorphisms.

Generalised Sheaf Cohomology Theories. The purpose of this book is to introduce the reader to the central part of category theory and to make the literature accessible to the reader who wishes Author: Rick Jardine.

2 homomorphisms. Thus H1.X et;/ D 2g, if is ﬁnite or is the l-adic integers Z H1.X et;Z/D0, for Zmust be given the discrete topology, and the image of any continuous map ˇalg 1.X;x/!Zis ore the etale cohomology is as expected in the ﬁrst two´ cases but is anomalous in the last.

It may seem that the etale topology should be superﬂuous when´ kis the complex num. Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology.Lecture 5.

Relation to Milnor K-Theory 29 Part 2. Etale Motivic Theory´ 35 Lecture 6. Etale sheaves with transfers 37´ Lecture 7.

The relative Picard group and Suslin’s Rigidity Theorem 47 Lecture 8. Derived tensor products 55 Appendix 8A. Tensor triangulated categories 63 Lecture 9. A1-weak equivalence 67 Etale´ A1-local complexes