Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104

by Eric M. Friedlander

Overview

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.

Product Details

ISBN-13:	9780691083179
Publisher:	Princeton University Press
Publication date:	12/21/1982
Series:	Annals of Mathematics Studies , #104
Pages:	191
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table of Contents

• Frontmatter, pg. 1
• INTRODUCTION, pg. 3
• 1. ETALE SITE OF A SIMPLICIAL SCHEME, pg. 7
• 2. SHEAVES AND COHOMOLOGY, pg. 13
• 3. COHOMOLOGY VIA HYPERCOVERINGS, pg. 20
• 4. ETALE TOPOLOGICAL TYPE, pg. 31
• 5. HOMOTOPY INVARIANTS, pg. 42
• 6. WEAK EQUIVALENCES, COMPLETIONS, AND HOMOTOPY LIMITS, pg. 51
• 7. FINITENESS AND HOMOLOGY, pg. 63
• 8. COMPARISON OF HOMOTOPY TYPES, pg. 70
• 9. APPLICATIONS TO TOPOLOGY, pg. 80
• 10. COMPARISON OF GEOMETRIC AND HOMOTOPY THEORETIC FIBRES, pg. 90
• 11. APPLICATIONS TO GEOMETRY, pg. 103
• 12. APPLICATIONS TO FINITE CHE VALLEY GROUPS, pg. 112
• 13. FUNCTION COMPLEXES, pg. 123
• 14. RELATIVE COHOMOLOGY, pg. 134
• 15. TUBULAR NEIGHBORHOODS, pg. 147
• 16. GENERALIZED COHOMOLOGY, pg. 158
• 17. POINCARÉ DUALITY AND LOCALLY COMPACT HOMOLOGY, pg. 170
• REFERENCES, pg. 184
• INDEX, pg. 188
• Backmatter, pg. 191