Noncommutative rigidity
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 extens...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg,
2018-07-25T18:06:52Z.
|
| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | 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 National Science Foundation (U.S.) (CAREER Award 1350472) Portuguese Science and Technology Foundation (Grant PEst-OE/MAT/UI0297/2014) |
|---|