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arXiv · 1901.06816

Twisted forms of perfect complexes and Hilbert 90

Ajneet Dhillon·Pál Zsámboki
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Abstract

Automorphisms of a perfect complex naturally have the structure of an $\infty$-group: the 1-morphisms are quasi-isomorphisms, the 2-morphisms are homotopies, etc. This article starts by proving some basic properties of this $\infty$-group. We go on to study the deformation theory of this stack of $\infty$-groups and give a criterion for this stack to be formally smooth. The classifying stack of this $\infty$-group classifies forms of a complex. We discuss a version of Hilbert 90 for perfect complexes.

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Ajneet Dhillon, Pál Zsámboki. 2019-01-21. Twisted forms of perfect complexes and Hilbert 90. https://arxiv.org/abs/1901.06816

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