Noncommutative Motives

2015 ◽  
Author(s):  
Gonçalo Tabuada
Keyword(s):  
Noncommutative Motives

scholarly journals Noncommutative motives, numerical equivalence, and semi-simplicity

2014 ◽  
Vol 136 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Matilde Marcolli ◽  
Gonçalo Tabuada
Keyword(s):  
Numerical Equivalence ◽  
Noncommutative Motives

scholarly journals Noncommutative motives of Azumaya algebras

2014 ◽  
Vol 14 (2) ◽  
pp. 379-403 ◽  
Author(s):  
Gonçalo Tabuada ◽  
Michel Van den Bergh
Keyword(s):  
Commutative Ring ◽  
Global Dimension ◽  
Azumaya Algebras ◽  
Finite Global Dimension ◽  
Finite Dimensional ◽  
Noncommutative Motives ◽  
Finite Dimensional Algebras ◽  
The Way

AbstractLet $k$ be a base commutative ring, $R$ a commutative ring of coefficients, $X$ a quasi-compact quasi-separated $k$-scheme, and $A$ a sheaf of Azumaya algebras over $X$ of rank $r$. Under the assumption that $1/r\in R$, we prove that the noncommutative motives with $R$-coefficients of $X$ and $A$ are isomorphic. As an application, we conclude that a similar isomorphism holds for every $R$-linear additive invariant. This leads to several computations. Along the way we show that, in the case of finite-dimensional algebras of finite global dimension, all additive invariants are nilinvariant.

scholarly journals $K$-theory of endomorphisms via noncommutative motives

2015 ◽  
Vol 368 (2) ◽  
pp. 1435-1465 ◽  
Author(s):  
Andrew J. Blumberg ◽  
David Gepner ◽  
Gonçalo Tabuada
Keyword(s):  
K Theory ◽  
Noncommutative Motives
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