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Noncommutative numerical motives, Tannakian structures, and motivic Galois groups

Matilde Marcolli, Gonçalo Tabuada (2016)

Journal of the European Mathematical Society

In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum ( k ) F of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum ( k ) F is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric...

Novikov homology, jump loci and Massey products

Toshitake Kohno, Andrei Pajitnov (2014)

Open Mathematics

Let X be a finite CW complex, and ρ: π 1(X) → GL(l, ℂ) a representation. Any cohomology class α ∈ H 1(X, ℂ) gives rise to a deformation γ t of ρ defined by γ t (g) = ρ(g) exp(t〈α, g〉). We show that the cohomology of X with local coefficients γ gen corresponding to the generic point of the curve γ is computable from a spectral sequence starting from H*(X, ρ). We compute the differentials of the spectral sequence in terms of the Massey products and show that the spectral sequence degenerates in case...

On a certain generalization of spherical twists

Yukinobu Toda (2007)

Bulletin de la Société Mathématique de France

This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of ( 0 , - 2 ) -curves on threefolds, or deforming ℙ -objects introduced by D.Huybrechts and R.Thomas.

On a conjecture of Kottwitz and Rapoport

Qëndrim R. Gashi (2010)

Annales scientifiques de l'École Normale Supérieure

We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.

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