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# Documents  Abbes, Ahmed | enregistrements trouvés : 6

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## Post-edited  The category MF in the semistable case Faltings, Gerd (Auteur de la Conférence) | CIRM (Editeur )

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

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## Post-edited  Interview at CIRM: Peter Scholze Scholze, Peter (Personne interviewée) | CIRM (Editeur )

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 ...

## Multi angle  The Witt vector affine Grassmannian Scholze, Peter (Auteur de la Conférence) | CIRM (Editeur )

(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.

## Multi angle  The characteristic cycle and the singular support of an étale sheaf Saito, Takeshi (Auteur de la Conférence) | CIRM (Editeur )

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.

## Multi angle  Non-minimal modularity lifting theorems for imaginary quadratic fields Calegari, Frank (Auteur de la Conférence) | CIRM (Editeur )

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.

## Multi angle  Construction of $p$-adic $L$-functions for unitary groups Harris, Michael (Auteur de la Conférence) | CIRM (Editeur )

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 ...

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