Stability of holonomicity over quasi-projective varieties

TL;DR

This paper proves Berthelot's conjectures on the stability of holonomicity for arithmetic D-modules over smooth projective formal schemes and constructs a stable category of complexes over quasi-projective varieties.

Contribution

It establishes the stability of holonomicity under six operations and builds a new category of complexes with bounded, F-holonomic cohomology.

Findings

Proves Berthelot's conjectures on holonomicity stability.

Constructs a stable category of arithmetic D-modules.

Demonstrates stability under Grothendieck's six operations.

Abstract

Let $\V$ be a mixed characteristic complete discrete valuation ring with perfect residue field $k$. We solve Berthelot's conjectures on the stability of the holonomicity over smooth projective formal $\V$-schemes. Then we build a category of complexes of arithmetic $\D$-modules over quasi-projective $k$-varieties with bounded, $F$-holonomic cohomology. We get its stability under Grothendieck's six operations.