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Peer-reviewedCC BYAdvances in Mathematics

Kaledin classes and formality criteria

  • Coline Emprin1,2
  1. 1DMA - Département de Mathématiques et Applications - ENS-PSL (UMR8553) (45 rue d'Ulm 75005 Paris - France)
  2. 2LAGA - Laboratoire Analyse, Géométrie et Applications (Institut Galilée, 99 avenue Jean-Baptiste Clément, F-93430, Villetaneuse, France - France)
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Abstract

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: outside 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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Cite

BibTeXRIS
BibTeX
@article{emprin2026kaledin,
  title = {{Kaledin classes and formality criteria}},
  author = {Coline Emprin},
  journal = {Advances in Mathematics},
  year = {2026},
  month = nov,
  doi = {10.1016/j.aim.2026.111376},
  url = {https://doi.org/10.1016/j.aim.2026.111376},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Kaledin classes and formality criteria
AU  - Coline Emprin
PY  - 2026
DA  - 2026/11/06
JO  - Advances in Mathematics
DO  - 10.1016/j.aim.2026.111376
UR  - https://doi.org/10.1016/j.aim.2026.111376
AB  - 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: outside 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.
SN  - 0001-8708
SN  - 1090-2082
ER  -