Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories
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1603.03411.pdf
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347.31 KB
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Author(s)
Trigo Neri Tabuada, Goncalo Jorge
Date Issued
November 2016
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Citation
Tabuada, Gonçalo. “Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories.” International Mathematics Research Notices (December 2016): rnw242
Version
Original manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNW242
