Generators in formal deformations of categories

Anthony Blanc, Ludmil Katzarkov, Pranav Pandit

Research output: Contribution to journalArticle

Abstract

In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a -linear -category for a field . Our main result states that if is a -linear -category which has a compact generator whose groups of self-extensions vanish for sufficiently high positive degrees, then every formal deformation of has zero curvature and moreover admits a compact generator.

Original languageEnglish (US)
Pages (from-to)2055-2089
Number of pages35
JournalCompositio Mathematica
Volume154
Issue number10
DOIs
StatePublished - Oct 1 2018
Externally publishedYes

Fingerprint

Generator
Vanish
Modulus
Curvature
Zero

Keywords

  • compact generators
  • deformation theory
  • dg-categories
  • E2 -algebras

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Generators in formal deformations of categories. / Blanc, Anthony; Katzarkov, Ludmil; Pandit, Pranav.

In: Compositio Mathematica, Vol. 154, No. 10, 01.10.2018, p. 2055-2089.

Research output: Contribution to journalArticle

Blanc, Anthony ; Katzarkov, Ludmil ; Pandit, Pranav. / Generators in formal deformations of categories. In: Compositio Mathematica. 2018 ; Vol. 154, No. 10. pp. 2055-2089.
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