Moduli spaces for $\Theta$-strata and non-reductive quotients

TL;DR

This paper provides a new proof for the existence of geometric quotients for graded unipotent group actions, extending previous results to more general settings including arbitrary characteristic and families.

Contribution

It introduces a novel proof approach using stacks of filtrations and gradings, generalizing the $ar{U}$-theorem to broader contexts.

Findings

Proof works over any affine Noetherian base.

Generalizes results to arbitrary characteristic.

Applies to actions in families and general $ heta$-strata.

Abstract

We give a new proof of the $\hat{U}$-theorem of B\'erczi, Doran, Hawes and Kirwan on the existence of geometric quotients for actions of graded unipotent groups in terms of stacks of filtrations and gradings introduced by Halpern-Leistner. Our proof works over any affine Noetherian base, in particular it simultaneously generalizes the previous results to arbitrary characteristic, actions in families and to general $\Theta$-strata.