Add to ORKGIn this article one extends the classical theory of (intermediate) Jacobians to the “noncommutative world”. Concretely, one constructs a Q-linear additive Jacobian functor N → J(N) from the category of noncommutative Chow motives to the category of abelian varieties up to isogeny, with the following properties: (i) the first de Rham cohomology group of J(N) agrees with the subspace of the odd periodic cyclic homology of N which is generated by algebraic curves; (ii) the abelian variety J(perf[subscript dg](X)) (associated to the derived dg category perf[subscript dg](X) of a smooth projective k-scheme X) identifies with the product of all the intermediate algebraic Jacobians of X. As an application, every semi-orthogonal decomposition of th...
This article is based on the lectures of the same tittle given by the first author during the instru...
This article is based on the lectures of the same tittle given by the first author during the instru...
In this note we relate the notions of Lefschetz type, decomposability, and isomorphism for Chow moti...
In this article one extends the classical theory of (intermediate) Jacobians to the “noncommutative ...
In this article, we introduce the category of noncommutative Artin motives as well as the category o...
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...
This survey is based on lectures given by the authors during the program “Noncommutative algebraic g...
30 pagesInternational audienceLet X and Y be complex smooth projective varieties, and D^b(X) and D^b...
30 pagesInternational audienceLet X and Y be complex smooth projective varieties, and D^b(X) and D^b...
17 Jul 2012 Original ManuscriptIn this article, we introduce the category of noncommutative Artin mo...
Making use of Hochschild homology, we introduce the correct category NNum(k)_F of noncommutative num...
Let X and Y be complex smooth projective varieties, and D[superscript b](X) and D[superscript b](Y) ...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
This article is based on the lectures of the same tittle given by the first author during the instru...
This article is based on the lectures of the same tittle given by the first author during the instru...
In this note we relate the notions of Lefschetz type, decomposability, and isomorphism for Chow moti...
In this article one extends the classical theory of (intermediate) Jacobians to the “noncommutative ...
In this article, we introduce the category of noncommutative Artin motives as well as the category o...
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...
This survey is based on lectures given by the authors during the program “Noncommutative algebraic g...
30 pagesInternational audienceLet X and Y be complex smooth projective varieties, and D^b(X) and D^b...
30 pagesInternational audienceLet X and Y be complex smooth projective varieties, and D^b(X) and D^b...
17 Jul 2012 Original ManuscriptIn this article, we introduce the category of noncommutative Artin mo...
Making use of Hochschild homology, we introduce the correct category NNum(k)_F of noncommutative num...
Let X and Y be complex smooth projective varieties, and D[superscript b](X) and D[superscript b](Y) ...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
In this article we prove that Kontsevich’s category NC_(num)(k)_F of noncommutative numerical motive...
This article is based on the lectures of the same tittle given by the first author during the instru...
This article is based on the lectures of the same tittle given by the first author during the instru...
In this note we relate the notions of Lefschetz type, decomposability, and isomorphism for Chow moti...