Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories

DOI10.1093/IMRN/RNW242zbMATH Open1405.14054arXiv1603.03411OpenAlexW2964124914MaRDI QIDQ4612101

Gonçalo Tabuada

Publication date: 22 January 2019

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: To every scheme, not necessarily smooth neither proper, we can associate its different mixed realizations (de Rham, Betti, etale, 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 dg categories. This leads to new additive invariants, 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.

Full work available at URL: https://arxiv.org/abs/1603.03411

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Motivic cohomology; motivic homotopy theory (14F42)

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