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Documents  Breuil, Christophe | enregistrements trouvés : 10

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Research talks;Algebraic and Complex Geometry;Number Theory

For smooth schemes the category $MF$ (defined by Fontaine for DVR's) realises the "mysterious functor", and provides natural systems of coeffients for crystalline cohomology. We generalise it to schemes with semistable singularities. The new technical features consist mainly of different methods in commutative algebra

14F30

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Outreach;Mathematics Education and Popularization of Mathematics

Peter Scholze became known as a mathematician after finishing his Bachelor's degree in three semesters and his Master's degree in two further semesters. Scholze's subsequent PhD-thesis on Perfectoid spaces yields the solution to a special case of the weight-monodromy conjecture.
He was made full professor shortly after completing his PhD, the youngest full professor in Germany.
Since July 2011 Scholze is a Fellow of the Clay Mathematics Institute. In 2012 he was awarded the Prix and Cours Peccot. He was awarded the 2013 SASTRA Ramanujan Prize. In 2014 he received the Clay Research Award. In 2015 he will be awarded the Frank Nelson Cole Prize in Algebra, and also the Ostrowski Prize.
According to the University of Bonn and to his peers, Peter is one of the most brilliant researchers in his field...
Peter Scholze became known as a mathematician after finishing his Bachelor's degree in three semesters and his Master's degree in two further semesters. Scholze's subsequent PhD-thesis on Perfectoid spaces yields the solution to a special case of the weight-monodromy conjecture.
He was made full professor shortly after completing his PhD, the youngest full professor in Germany.
Since July 2011 Scholze is a Fellow of the Clay Mathematics ...

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Research talks;Algebraic and Complex Geometry;Number Theory

(joint with Bhargav Bhatt) We prove that the space of $W(k)$-lattices in $W(k)[1/p]^n$, for a perfect field $k$ of characteristic $p$, has a natural structure as an ind-(perfect scheme). This improves on recent results of Zhu by constructing a natural ample line bundle on the space of such lattices.

13F35 ; 14G22 ; 14F30

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Research talks;Algebraic and Complex Geometry;Number Theory

We define the characteristic cycle of an étale sheaf on a smooth variety of arbitrary dimension in positive characteristic using the singular support, constructed by Beilinson very recently. The characteristic cycle satisfies a Milnor formula for vanishing cycles and an index formula for the Euler-Poincaré characteristic.

14F20 ; 14G17 ; 11S15

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Research talks;Algebraic and Complex Geometry;Number Theory

I will explain how previous (conditional) minimal modularity lifting results (in the presence of torsion) may be adapted to the non-minimal case in the context of imaginary quadratic fields. This is joint work with David Geraghty.

11F33 ; 11F80 ; 14K15

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Research talks;Algebraic and Complex Geometry;Number Theory

This is a report on the construction of $p$-adic $L$-functions attached to ordinary families of holomorphic modular forms on the unitary groups of $n$-dimensional hermitian vector spaces over $CM$ fields. The results have been obtained over a period of nearly 15 years in joint work with Ellen Eischen, Jian-Shu Li, and Chris Skinner. The $p$-adic $L$-functions specialize at classical points to critical values of standard $L$-functions of cohomological automorphic forms on unitary groups, or equivalently of cohomological automorphic forms on $GL(n)$ that satisfy a polarization condition. When $n = 1$ one recovers Katz's construction of $p$-adic $L$-functions of Hecke characters. This is a report on the construction of $p$-adic $L$-functions attached to ordinary families of holomorphic modular forms on the unitary groups of $n$-dimensional hermitian vector spaces over $CM$ fields. The results have been obtained over a period of nearly 15 years in joint work with Ellen Eischen, Jian-Shu Li, and Chris Skinner. The $p$-adic $L$-functions specialize at classical points to critical values of standard $L$-functions of ...

11F33 ; 11R23 ; 14G35

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- v; 114 p.
ISBN 978-0-8218-5227-9

Memoirs of the american mathematical society , 1016

Localisation : Collection 1er étage

représentation de groupes # corps locaux # théorie de Galois # correspondance de Langlands mod p # poids de Serre

22E50 ; 11F80 ; 11F70

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- x, 473 p.
ISBN 978-2-85629-282-2

Astérisque , 0331

Localisation : Périodique 1er étage

Correspondance de Langlands locale # (phi, gamma)-modules # anneaux de Fontaine # représentations unitaires

11Fxx ; 11Sxx

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- xxiii, 557 p.
ISBN 978-2-85629-281-5

Astérisque , 0330

Localisation : Périodique 1er étage

Correspondance de Langlands locale # (phi, gamma)-modules # anneaux de Fontaine # représentations unitaires

11Fxx ; 11Sxx

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- xv; 420 p.
ISBN 978-2-85629-256-3

Astérisque , 0319

Localisation : Périodique 1er étage;Réserve

équations différentielles p-adiques # actions de Frobenius # anneau de Robba # anneaux de Fontaine # Banach # cohomologie étale # faisceaux de Fontaine # familles de représentations p-adiques # filtrations de pentes # isomorphismes de comparaison # p-adiques # représentations p-adiques # semi-stable # théorie de Hodge p-adique # théorie de Sen # topologie de Grothendieck

11F80 ; 11G99 ; 11S05 ; 11S15 ; 11S20 ; 11S80 ; 12H25 ; 13K05 ; 14E22 ; 14F20 ; 14F30

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