Automorphisms of perfect complexes
Dhillon, Ajneet ; Zsámboki, Pál
arXiv, Tome 2019 (2019) no. 0, / Harvested from
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, and a homotopical Skolem--Noether theorem.
Publié le : 2019-01-21
Classification:  Mathematics - Algebraic Geometry 
@article{1901.06816,
     author = {Dhillon, Ajneet and Zs\'amboki, P\'al},
     title = {Automorphisms of perfect complexes},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.06816}
}

Dhillon, Ajneet; Zsámboki, Pál. Automorphisms of perfect complexes. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.06816/