Algebraicity and smoothness of fixed point stacks
Matthieu Romagny (IRMAR)
TL;DR
This paper investigates the algebraic and smooth structure of fixed point stacks under certain group schemes, extending classical theorems to broader contexts involving non-flat groups acting on algebraic stacks.
Contribution
It extends foundational theorems on functors of homomorphisms and reductive subgroups to non-flat group schemes acting on algebraic stacks.
Findings
Established algebraicity of fixed point stacks under specified conditions
Proved smoothness results for fixed point stacks with reductive or proper factors
Extended classical theorems to non-flat group schemes in algebraic geometry
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology