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Some new directions in p -adic Hodge theory

Kiran S. Kedlaya (2009)

Journal de Théorie des Nombres de Bordeaux

We recall some basic constructions from p -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B -pairs, introduced recently by Berger, which provides a natural enlargement of the category of p -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology, including Tate...

Spherical roots of spherical varieties

Friedrich Knop (2014)

Annales de l’institut Fourier

Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.

Stably rational algebraic tori

Valentin E. Voskresenskii (1999)

Journal de théorie des nombres de Bordeaux

The rationality of a stably rational torus with a cyclic splitting field is proved.

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