Modified mixed realizations, new additive invariants, and periods of DG categories

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

To every scheme, not necessarily smooth neither proper, we can associate its different mixed realizations (de Rham, Betti, étale, Hodge, etc.) as well as its ring of periods. In this note, following an insight of Kontsevich, we prove that, after suitable modifications, these classical constructions can be extended from schemes to the broad setting of differential graded (dg) categories. This leads to new additive invariants of dg categories, which we compute in the case of differential operators, as well as to a theory of periods of dg categories. Among other applications, we prove that the ring of periods of a scheme is invariant under projective homological duality. Along the way, we explicitly describe the modified mixed realizations using the Tannakian formalism.

Original languageEnglish
Pages (from-to)7607-7638
Number of pages32
JournalInternational Mathematics Research Notices
Volume2017
Issue number24
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • K-THEORY
  • NONCOMMUTATIVE MOTIVES
  • A(1)-HOMOTOPY THEORY
  • MODULES

Fingerprint Dive into the research topics of 'Modified mixed realizations, new additive invariants, and periods of DG categories'. Together they form a unique fingerprint.

  • Cite this