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  3. Sheaves and Functions Modulo p
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  • Publisher:
    Cambridge University Press
    Publication date:
    05 November 2015
    05 November 2015
    ISBN:
    9781316480687
    9781316502594
    DOI:
    https://doi.org/10.1017/CBO9781316480687
    Dimensions:
    Weight & Pages:
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.21kg, 131 Pages
    • Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (429)
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (429)
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    Book description

    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.

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