D-affinity and Frobenius morphism on quadrics

TL;DR

This paper analyzes the decomposition of Frobenius push-forwards of line bundles on quadrics, identifying conditions for tilting bundles and exploring applications to D-modules.

Contribution

It provides explicit decompositions of Frobenius push-forwards on quadrics and characterizes when these form tilting bundles, advancing understanding of D-modules in this context.

Findings

Decomposition of Frobenius push-forwards into line and spinor bundles

Conditions under which Frobenius push-forward yields tilting bundles

Applications to the study of D-modules on quadrics

Abstract

We compute decomposition of Frobenius push-forwards of line bundles on quadrics into a direct sum of line bundles and spinor bundles. As an application we show when the Frobenius push-forward gives a tilting bundle and we apply it to study D-modules on quadrics.