Romagny — Algebraicity And Smoothness Of Fixed Point Stacks (2022)

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Matthieu Romagny. Algebraicity and Smoothness of Fixed Point Stacks. arXiv. 2022.

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Abstract

We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine, finitely presented diagonal. For this, we extend some theorems of [SGA3.2] on functors of homomorphisms Hom(G, H) and functors of reductive subgroups Sub(H) for an affine, possibly non-flat group scheme H.