Pré-Publication, Document De Travail Année : 2024

Kaledin classes and formality criteria

Classes de Kaledin et critères de formalité

Résumé

We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded algebras over operads or properads, possibly colored in groupoids. The present treatment generalizes the previous obstruction classes in two directions: beyond characteristic zero and including a wider range of algebraic structures. This enables us to establish novel formality criteria, including formality descent with torsion coefficients, formality in families, intrinsic formality, and criteria in terms of chain-level lifts of homology automorphism.

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Dates et versions

hal-05273226 , version 1 (22-09-2025)

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Coline Emprin. Kaledin classes and formality criteria. 2024. ⟨hal-05273226⟩
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