Noncommutative rigidity
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Author(s)
Trigo Neri Tabuada, Goncalo Jorge
Date Issued
November 2017
Journal
Mathematische Zeitschrift
Publisher
Springer Berlin Heidelberg
Citation
Tabuada, Gonçalo. “Noncommutative Rigidity.” Mathematische Zeitschrift, vol. 289, no. 3–4, Aug. 2018, pp. 1281–98.
Version
Author's final manuscript
Abstract
In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of separably closed fields. As a byproduct, we obtain an extension of Suslin’s rigidity theorem, as well as of Yagunov-Østvær’s equivariant rigidity theorem, to singular varieties. Among other applications, we show that base-change along primary field extensions yields a faithfully flat morphism between noncommutative motivic Galois groups. Finally, along the way, we introduce the category of n-adic noncommutative mixed motives. Keywords: Algebraic cycles, K-theory, noncommutative algebraic geometry
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/10.1007/s00209-017-1998-5
