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Subjects
14-XX Algebraic geometry
14Gxx Arithmetic problems. Diophantine geometry
14G35 Modular and Shimura varieties

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Galois orbits and equidistribution: Manin-Mumford and André-Oort.

Andrei Yafaev (2009)

Journal de Théorie des Nombres de Bordeaux

We overview a unified approach to the André-Oort and Manin-Mumford conjectures based on a combination of Galois-theoretic and ergodic techniques. This paper is based on recent work of Klingler, Ullmo and Yafaev on the André-Oort conjecture, and of Ratazzi and Ullmo on the Manin-Mumford conjecture.

Galois representations modulo p and cohomology of Hilbert modular varieties

Mladen Dimitrov (2005)

Annales scientifiques de l'École Normale Supérieure

Geometry of an étale covering of the $p$ -adic upper half plane

Jeremy Teitelbaum (1990)

Annales de l'institut Fourier

We describe the rigid geometry of the first layer in the tower of coverings of the $p$ -adic upper half plane constructed by Drinfeld. Using our results, we describe the stable fiber at p of certain Shimura curves.

Currently displaying 1 – 3 of 3