Geometry of p-adically uniformized varieties

Ponente: Ehud de Shalit
Institución: The Hebrew University of Jerusalem
Tipo de Evento: Researcher

When	Sep 01, 2015 from 12:00 PM to 01:00 PM
Where	Auditorio "Alfonso Nápoles Gándara"
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Abstract:

P-adic numbers were invented by Hensel to encode solutions to congruences modulo all powers of a prime number p. "Soft" p-adic analysis allows one to talk about p-adic manifolds, p-adic Lie groups etc., but a major obstacle is that the p-adic world is totally disconnected. This was overcome by Tate in the 1960's, with the invention of Rigid Analytic Geometry.

Quotients of p-adic symmetric domains by discrete groups of automorphisms can be algebraized, as was done by Klein, Fuchs and Poincare in the classical setting. The ensuing class of p-adically uniformized varieties has important applications to number theory.

We shall survey this line of development, ending with results of the speaker from 2005 on the Monodromy-Weight conjecture for p-adically unifromized varieties.