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arithmetic D-module

Contents

Idea

The theory of arithmetic D-modules was primarily developped by Berthelot to better understand the functoriality properties of rigid cohomology. It gives a theory of coefficients for the cohomology of quasi-projective algebraic varieties over finite fields that are stable by the six Grothendieck operations, after Kedlaya and Caro. This allows a purely p-adic proof of Deligne’s Weil II theorem, that generalized the Riemann hypothesis over finite fields to the category of coefficients for cohomology (i.e., motivic sheaves).

References

Revised on February 16, 2014 08:11:54 by Urs Schreiber (89.204.155.248)