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arXiv · 1810.08570

Deformations of algebraic schemes via Reedy-Palamodov cofibrant resolutions

Marco Manetti·Francesco Meazzini
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Abstract

Let $X$ be a Noetherian separated and finite dimensional scheme over a field $\mathbb{K}$ of characteristic zero. The goal of this paper is to study deformations of $X$ over a differential graded local Artin $\mathbb{K}$-algebra by using local Tate-Quillen resolutions, i.e., the algebraic analog of the Palamodov's resolvent of a complex space. The above goal is achieved by describing the DG-Lie algebra controlling deformation theory of a diagram of differential graded commutative algebras, indexed by a direct Reedy category.

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Marco Manetti, Francesco Meazzini. 2018-10-19. Deformations of algebraic schemes via Reedy-Palamodov cofibrant resolutions. https://doi.org/10.1016/j.indag.2019.08.007

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