Un scindage de l'application de Frobenius sur toute l'alg\`ebre des distributions de SL_2

TL;DR

This paper investigates a splitting of the Frobenius map on the entire algebra of distributions of SL_2 over finite fields and explores its connection with Frobenius descent in arithmetic D-modules on the projective line.

Contribution

It introduces a novel splitting of the Frobenius map on the algebra of distributions of SL_2 and relates it to Frobenius descent in arithmetic D-modules.

Findings

Established a splitting of Frobenius on the algebra of distributions of SL_2

Linked the splitting to explicit Frobenius descent on arithmetic D-modules

Provided new insights into the structure of distributions over SL_2

Abstract

We study a splitting of the Frobenius map on the whole algebra of distributions of SL_2 (over a finite field) and its relation with the explicit Frobenius descent on arithmetic D-modules over the projective line