Theory of weights in p-adic cohomology

TL;DR

This paper develops a theory of weights for overholonomic complexes of arithmetic D-modules over finite fields, mirroring Deligne's l-adic framework, with key properties preserved under six operations and intermediate extensions.

Contribution

It introduces a new weight theory for arithmetic D-modules with Frobenius structure, extending properties analogous to Deligne's weights in l-adic cohomology.

Findings

Weights are preserved under six operations.

Intermediate extension preserves pure complexes and weights.

The theory aligns with Deligne's weight framework.

Abstract

Let k be a finite field of characteristic p>0. We construct a theory of weights for overholonomic complexes of arithmetic D-modules with Frobenius structure on varieties over k. The notion of weight behave like Deligne's one in the l-adic framework: first, the six operations preserve weights, and secondly, the intermediate extension of an immersion preserves pure complexes and weights.