arXiv subjects

Pascal Boyer

Publications and source records attributed to Pascal Boyer.

23 records · Page 2Linked to original sources

arXiv2014

Filtrations de stratification de quelques variétés de Shimura simples

We define and study new filtrations called of stratification of a perverse sheaf on a scheme; beside the cases of the weight or monodromy filtrations, these filtrations are available whatever are the ring of coefficients. We illustrate these constructions in the geometric situation of the simple unitary Shimura varieties of Harris and Taylor's book for the perverse sheaves of Harris-Taylor and the complex of vanishing cycles, introduced and studied in my 2009 paper at inventiones. In the situation studied in loc. cit., we show how to use these filtrations to simplify the principal step of this paper; the cases of finite field or ring of integer of a local field will be studied in the next published paper.

math.AG↗

arXiv2008

Réseaux d'induction des représentations elliptiques de Lubin-Tate

We study the reduction modulo $l$ of some elliptic representations; for each of these representations, we give a particular lattice naturally obtained by parabolic induction in giving the graph of extensions between its irreducible sub-quotient of its reduction modulo $l$. The principal motivation for this work, is that these lattices appear in the cohomology of Lubin-Tate towers.

math.RT↗

arXiv2007

On the irreductibility of some Igusa varieties

We describe the connected components of Igusa's varieties of second species defined par Harris and Taylor in their book. There are in bijection with the characters of the inversible group of the maximal order of the division algebra attached to them.

math.NT↗

arXiv2006

Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications

In the geometric situation of the simple Shimura varieties of Kottwitz studied in Harris and Taylor's book, we describe the monodromy filtration of the vanishing cycles complex and the spectral sequence associated to it. We prove in particular that this filtration coincides with the weight one up to shift. Thanks to the Berkovich-Fargues' theorem, we deduce the description of the local monodromy filtration of the Deligne-Carayol model. In application, we obtain the description of the local components of cohomological automorphic representations of certains unitary groups, a global Jacquet-Langlands correspondence between two such groups and a proof of the weight-monodromy conjecture for the cohomology of these Shimura varieties.

math.AG↗

arXiv2006

Faisceaux pervers des cycles évanescents des variétés de Drinfeld et groupes de cohomologie du modèle de Deligne-Carayol

In the first half of the paper, we translate in the geometric situation of Drinfeld varieties, the principal results of the Harris and Taylor's book. We give in particular the restriction to the open strata of the vanishing cycles sheaves in terms of some local systems named Harris-Taylor's local systems which we calculate the alternated sum of the cohomology group with compact supports. In the last half of the paper, we describe the monodromy filtration of the vanishing cycles perverse sheaf and the spectral sequence associated to it. Thanks to the Berkovich-Fargues' theorem, we obtain the description of the local monodromy filtration of the Deligne-Carayol model.

math.AG↗