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The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves corresponding to local systems on a smooth, projective curve $C$ to the case of local systems with indecomposable unipotent ramification at a finite set of points. To this end we need an extension of the notion of parabolic structure on vector bundles to coherent sheaves. Once we have defined this, a lot of arguments from the article “ On the geometric Langlands conjecture” by Frenkel, Gaitsgory and Vilonen [11]...

Cohomolgie des variétés de modules de hauteur nulle.

J.-M. Drezet (1988)

Mathematische Annalen

Cohomologial dimension of Laumon 1-motives up to isogenies

Nicola Mazzari (2010)

Journal de Théorie des Nombres de Bordeaux

We prove that the category of Laumon 1-motives up to isogenies over a field of characteristic zero is of cohomological dimension $\leq 1$ . As a consequence this implies the same result for the category of formal Hodge structures of level $\leq 1$ (over $ℚ$ ).

Cohomological descent of rigid cohomology for étale coverings

Bruno Chiarellotto, Nobuo Tsuzuki (2003)

Rendiconti del Seminario Matematico della Università di Padova

Cohomological dimension filtration and annihilators of top local cohomology modules

Ali Atazadeh, Monireh Sedghi, Reza Naghipour (2015)

Colloquium Mathematicae

Let denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration $= {M_{i}}_{i = 0}^{c}$ , where c = cd(,M) and $M_{i}$ denotes the largest submodule of M such that $c d (, M_{i}) \leq i$ . Some properties of this filtration are investigated. In particular, if (R,) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module $H_{}^{c} (M)$ , namely $A n n_{R} (H_{}^{c} (M)) = A n n_{R} (M / M_{c - 1})$ . As a consequence, there exists an ideal of R such that $A n n_{R} (H_{}^{c} (M)) = A n n_{R} (M / H ⁰_{} (M))$ . This generalizes the main results...