Brylinski-Radon transformation in characteristic $p>0$

TL;DR

This paper characterizes the Brylinski-Radon transform in positive characteristic using Beilinson's singular support theory, offers an alternative proof over complex numbers, and introduces a microlocal criterion for perverse sheaves.

Contribution

It extends Brylinski's results to characteristic p>0 and provides new microlocal criteria for sheaf descent, broadening the transform's applicability.

Findings

Characterization of Brylinski-Radon transform in characteristic p>0

Alternative proof of Brylinski's results over complex numbers

Microlocal criterion for descent of perverse sheaves

Abstract

In this article, we characterize the image of the Brylinski-Radon transform in characteristic $p>0$ via Beilinson's theory of singular supports. We also provide an alternate proof of Brylinski's results over $\mathbb{C}$, which also works for sheaves with finite coefficients. Along the way, we also obtain a microlocal criterion for the descent of perverse sheaves which could be of independent interest.