Ludwig Modin (Leibniz Universität Hannover): Moduli spaces for Theta-strata and non-reductive quotients

The U-hat theorem of Bérczi, Doran, Hawes and Kirwan gives conditions for when a linear action of a complex graded unipotent group admits a geometric quotient, it is one of the key results non-reductive geometric invariant theory is built on.
We give a stacky re-interpretation of this theorem in terms of Theta-strata, as introduced by Halpern-Leistner, of algebraic stacks. As a corollary we generalize the U-hat theorem to not necessarily linear actions of graded unipotent groups over a Noetherian base scheme.

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