Sheaves and Functions Modulo p: Lectures on the Woods Hole Trace Formula: 429 (London Mathematical Society Lecture Note Series, Series Number 429)

Taelman, Lenny

ISBN 10: 1316502597 / ISBN 13: 9781316502594

Published by Cambridge University Press, 2015

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Bibliographic Details

• Title: Sheaves and Functions Modulo p: Lectures on the Woods Hole Trace Formula: 429 (London Mathematical Society Lecture Note Series, Series Number 429)
• Publisher: Cambridge University Press
• Publication Date: 2015
• Language: English
• ISBN 10: 1316502597
• ISBN 13: 9781316502594
• Binding: Paperback
• Condition: Very Good

About this title

Synopsis

The Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheaves-functions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields to coherent modules equipped with a Frobenius structure. This book begins with a short introduction to the homological theory of crystals of Böckle and Pink with the aim of introducing the sheaves-functions dictionary as quickly as possible, illustrated with elementary examples and classical applications. Subsequently, the theory and results are expanded to include infinite coefficients, L-functions, and applications to special values of Goss L-functions and zeta functions. Based on lectures given at the Morningside Center in Beijing in 2013, this book serves as both an introduction to the Woods Hole trace formula and the sheaves-functions dictionary, and to some advanced applications on characteristic p zeta values.

About the Author

Lenny Taelman is Professor of Algebraic Geometry at the University of Amsterdam.