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THE p-COHOMOLOGY OF ALGEBRAIC VARIETIES AND SPECIAL VALUES OF ZETA FUNCTIONS

Published online by Cambridge University Press:  02 June 2014

James S. Milne
Affiliation:
Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA ([email protected]) URL: www.jmilne.org/math/
Niranjan Ramachandran
Affiliation:
Mathematics Department, University of Maryland, College Park, MD 20742, USA ([email protected]) URL: www2.math.umd.edu/∼atma/

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 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 $p$.

Type
Research Article
Copyright
© Cambridge University Press 2014 

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