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

摘要

The p-cohomology of an algebraic variety in characteristic p lies naturallyin the category $D_{c}^{b}(R)$ of coherent complexes of graded modules over theRaynaud ring (Ekedahl-Illusie-Raynaud). We study homological algebra in thiscategory. When the base field is finite, our results provide relations betweenthe the absolute cohomology groups of algebraic varieties, log varieties,algebraic stacks, etc. and the special values of their zeta functions. Theseresults provide compelling evidence that $D_{c}^{b}(R)$ is the correct targetfor p-cohomology in characteristic p.