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 Boeckle 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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