The p-cohomology of algebraic varieties and special values of zeta functions

Abstract

The p-cohomology of an algebraic variety in characteristic p lies naturally in the category $D_c^b(R)$ of coherent complexes of graded modules over the Raynaud ring (Ekedahl-Illusie-Raynaud). We study homological algebra in this category. When the base field is finite, our results provide relations between the the absolute cohomology groups of algebraic varieties, log varieties, algebraic stacks, etc. and the special values of their zeta functions. These results provide compelling evidence that $D_c^b(R)$ is the correct target for p-cohomology in characteristic p.

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References in corpus (3)

• Triangulated categories of mixed motives
• Decomposition Theorem for Perverse sheaves on Artin stacks over finite fields
• Motivic complexes and special values of zeta functions

Cited by in corpus (4)

• Duality for cohomology of curves with coefficients in abelian varieties
• Motivic complexes and special values of zeta functions
• On the $\mu$-invariants of abelian varieties over function fields of positive characteristic
• Tamagawa number formula with coefficients over varieties in positive characteristic