Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104 / Eric M. Friedlander.

Format:

Book

Author/Creator:

Friedlander, Eric M., author.

Series:

Annals of mathematics studies ; Number 104.

Annals of Mathematics Studies ; 231

Language:

English

Subjects (All):

Homotopy theory.

Schemes (Algebraic geometry).

Homology theory.

Physical Description:

1 online resource (193 pages).

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions.One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.

Contents:

Frontmatter

INTRODUCTION

1. ETALE SITE OF A SIMPLICIAL SCHEME

2. SHEAVES AND COHOMOLOGY

3. COHOMOLOGY VIA HYPERCOVERINGS

4. ETALE TOPOLOGICAL TYPE

5. HOMOTOPY INVARIANTS

6. WEAK EQUIVALENCES, COMPLETIONS, AND HOMOTOPY LIMITS

7. FINITENESS AND HOMOLOGY

8. COMPARISON OF HOMOTOPY TYPES

9. APPLICATIONS TO TOPOLOGY

10. COMPARISON OF GEOMETRIC AND HOMOTOPY THEORETIC FIBRES

11. APPLICATIONS TO GEOMETRY

12. APPLICATIONS TO FINITE CHE VALLEY GROUPS

13. FUNCTION COMPLEXES

14. RELATIVE COHOMOLOGY

15. TUBULAR NEIGHBORHOODS

16. GENERALIZED COHOMOLOGY

17. POINCARÉ DUALITY AND LOCALLY COMPACT HOMOLOGY

REFERENCES

INDEX

Backmatter

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881499

1400881498

OCLC:

979882335