Author(s)Trigo Neri Tabuada, Goncalo Jorge
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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
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Springer Berlin Heidelberg
Tabuada, Gonçalo. “Noncommutative Rigidity.” Mathematische Zeitschrift, vol. 289, no. 3–4, Aug. 2018, pp. 1281–98.
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