Unifying derived deformation theories

Research output: Contribution to journalArticlepeer-review

Abstract

We develop a framework for derived deformation theory, valid in all characteristics. This gives a model category reconciling local and global approaches to derived moduli theory. In characteristic 0, we use this to show that the homotopy categories of DGLAs and SHLAs (. L∞-algebras) considered by Kontsevich, Hinich and Manetti are equivalent, and are compatible with the derived stacks of Toën-Vezzosi and Lurie. Another application is that the cohomology groups associated to any classical deformation problem (in any characteristic) admit the same operations as André-Quillen cohomology.
Original languageEnglish
Pages (from-to)772-826
Number of pages55
JournalAdvances in Mathematics
Volume224
Issue number3
DOIs
Publication statusPublished - 1 Jun 2010

Keywords

  • Deformation theory
  • Derived moduli

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