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Mathematics > Commutative Algebra
Title: An equivariant BGG correspondence and perfect complexes for extensions by $\mathbb{Z}/2\times \mathbb{Z}/2$
(Submitted on 16 Apr 2024)
Abstract: We provide an equivariant extension of Carlsson's BGG correspondence in characteristic two. As an application we classify perfect cochain complexes of $(\mathbb{Z}/2\times \mathbb{Z}/2)\rtimes Q$-representations with four-dimensional total homology for finite groups $Q$ of odd order. We deduce that cochain complexes of finite, free $A_4$-CW complexes with four-dimensional total homology are rigid: They are determined by the degrees of the nonzero homology groups.
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