Frobenius Push-Forwards on Quadrics

TL;DR

This paper generalizes and simplifies Langer's results on Frobenius direct images of line bundles on quadrics, explicitly decomposing higher Frobenius push-forwards of Cohen-Macaulay bundles, with special focus on characteristic two, and examines their tilting properties.

Contribution

It provides explicit decompositions of Frobenius push-forwards of bundles on quadrics, extending Langer's work and analyzing tilting conditions in characteristic two.

Findings

Explicit decompositions of Frobenius push-forwards on quadrics.

Identification of tilting Frobenius push-forwards of the structure sheaf.

Simplification and generalization of existing results.

Abstract

We generalize, explain and simplify Langer's results concerning Frobenius direct images of line bundles on quadrics, describing explicitly the decompositions of higher Frobenius push-forwards of arithmetically Cohen-Macaulay bundles into indecomposables, with an additional emphasis on the case of characteristic two. These results are applied to check which Frobenius push-forwards of the structure sheaf are tilting.