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Nombre de programmes trouvés : 806
Conférences

le (1h1m14s)

A. von Pippich - An analytic class number type formula for PSL2(Z)

For any Fuchsian subgroup Γ⊂PSL2(R) of the first kind, Selberg introduced the Selberg zeta function in analogy to the Riemann zeta function using the lengths of simple closed geodesics on Γ∖H instead of prime numbers. In this talk, we report on a formula that determines the special value at s=1 of the derivative of the Selberg zeta function for Γ=PSL2(Z). This formula is obtained as an application of a generalized Riemann-Roch isometry for the trivial sheaf on ¯¯¯¯¯¯¯¯¯¯¯Γ∖H, equipped with the Poincaré metric. This is joint ...
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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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Cours magistraux

le (1h26m53s)

J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part2)

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of sections of V is the non-negative real number h0θ(E,∥.∥):=log∑v∈Ee−π∥v∥2. In these lectures, I will firstly discuss diverse properties of the invariant h0θ and of its extensions to certain infinite dimensional generalizations of Euclidean lattices. Then I will present ...
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Cours magistraux

le (1h31m5s)

J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1)

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of sections of V is the non-negative real number h0θ(E,∥.∥):=log∑v∈Ee−π∥v∥2. In these lectures, I will firstly discuss diverse properties of the invariant h0θ and of its extensions to certain infinite dimensional generalizations of Euclidean lattices. Then I will present ...
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