Tate duality in positive dimension over function fields / Zev Rosengarten.

Format:

Book

Author/Creator:

Rosengarten, Zev, author.

Series:

Memoirs of the American Mathematical Society ; 0065-9266 no.1444.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1444

Language:

English

Subjects (All):

Algebraic fields.

Physical Description:

v, 217 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all affine commutative group schemes of finite tyep, building on the recent work of Česnavičius ("Poitou-Tate without restrictions on the order," 2015) extending these results to all finite commutative group schemes. We concentrate mainly on the more difficult function field setting, giving some remarks about the number field case along the way.

Contents:

Chapter 1. Introduction and main results

Chapter 2. General fields

Chapter 3. Local fields

Chapter 4. Local integral cohomology

Chapter 5. Global fields

Appendix A. Products and ultraproducts

Appendix B. Valuation rings

Appendix C. Profinite completions

Appendix D. Duality pairings and Weil restriction

Appendix E. Cohomology and direct limits

Appendix F. Compatibility between Čech and derived functor constructions

Appendix G. Characteristic 0

Bibliography,

Notes:

"October 2023, volume 290, number 1444 (fourth of 5 numbers)"

Includes bibliographical references (pages 215-217).

ISBN:

9781470467074

1470467070

OCLC:

1416882350