Add to ORKGMaking use of Hochschild homology, we introduce the correct category NNum(k)_F of noncommutative numerical motives (over a base ring k and with coefficients in a field F). We prove that NNum(k)_F is abelian semi-simple and that Grothendieck’s category Num(k)_Q of numerical motives embeds into NNum(k)_Q after being factored out by the action of the Tate object. As an application we obtain an alternative proof of Jannsen’s celebrate semi-simplicity result, which uses the noncommutative world instead of a classical Weil cohomology
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology...
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology...
This article is based on the lectures of the same tittle given by the first author during the instru...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
This survey is based on lectures given by the authors during the program “Noncommutative algebraic g...
In this article, we introduce the category of noncommutative Artin motives as well as the category o...
17 Jul 2012 Original ManuscriptIn this article, we introduce the category of noncommutative Artin mo...
This survey is based on lectures given by the authors during the program “Noncommutative algebraic g...
In this article we prove that Kontsevich’s category NC[subscript num](k)[subscript F] of noncommutat...
In this article, we introduce the category of noncommutative Artin motives as well as the category o...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology...
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology...
This article is based on the lectures of the same tittle given by the first author during the instru...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
This survey is based on lectures given by the authors during the program “Noncommutative algebraic g...
In this article, we introduce the category of noncommutative Artin motives as well as the category o...
17 Jul 2012 Original ManuscriptIn this article, we introduce the category of noncommutative Artin mo...
This survey is based on lectures given by the authors during the program “Noncommutative algebraic g...
In this article we prove that Kontsevich’s category NC[subscript num](k)[subscript F] of noncommutat...
In this article, we introduce the category of noncommutative Artin motives as well as the category o...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By ...
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology...
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology...
This article is based on the lectures of the same tittle given by the first author during the instru...