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Integral representations for solutions of exponential Gauß-Manin systems

Marco Hien, Céline Roucairol (2008)

Bulletin de la Société Mathématique de France

Let f , g : U → 𝔸 1 be two regular functions from the smooth affine complex variety U to the affine line. The associated exponential Gauß-Manin systems on the affine line are defined to be the cohomology sheaves of the direct image of the exponential differential system 𝒪 U e g with respect to f . We prove that its holomorphic solutions admit representations in terms of period integrals over topological chains with possibly closed support and with rapid decay condition.

Linear free divisors and the global logarithmic comparison theorem

Michel Granger, David Mond, Alicia Nieto-Reyes, Mathias Schulze (2009)

Annales de l’institut Fourier

A complex hypersurface D in ℂ n is a linear free divisor (LFD) if its module of logarithmic vector fields has a global basis of linear vector fields. We classify all LFDs for n at most 4 .By analogy with Grothendieck’s comparison theorem, we say that the global logarithmic comparison theorem (GLCT) holds for D if the complex of global logarithmic differential forms computes the complex cohomology of ℂ n ∖ D . We develop a general criterion for the GLCT for LFDs and prove that it is fulfilled whenever the...

Nonabelian Hodge theory in characteristic p

A. Ogus, V. Vologodsky (2007)

Publications Mathématiques de l'IHÉS

Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.

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...

Currently displaying 61 – 80 of 124