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Nombre de programmes trouvés : 18753
Cours magistraux

le (1h30m57s)

F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part2)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, ...
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Cours magistraux

le (1h24m57s)

J. Bruinier et J. Ignacio Burgos Gil - Arakelov theory on Shimura varieties (part2)

A Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties have a very rich geometric and arithmetic structure. For instance they are defined over a number field (the reflex field), they have line bundles provided with hermitian metrics that come from a representation of a maximal compact subgroup and sometimes they have models over a localization of a ring of integers ...
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Conférences

le (1h3m1s)

Y. Tang - Exceptional splitting of reductions of abelian surfaces with real multiplication

Chavdarov and Zywina showed that after passing to a suitable field extension, every abelian surface A with real multiplication over some number field has geometrically simple reduction modulo p for a density one set of primes p. One may ask whether its complement, the density zero set of primes p such that the reduction of A modulo p is not geometrically simple, is infinite. Such question is analogous to the study of exceptional mod p isogeny between two elliptic curves in the recent work of Charles. ...
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