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Seminario Dottorato: Analytic and algebraic varieties: the classical and the non archimedean case

Tuesday 13 April 2010 - Alice Ciccioni

ARGOMENTI: Seminari Dottorato

SEMINARIO DOTTORATO
Tuesday 13 April 2010 h. 14:30, room 1A/150
Alice Ciccioni (Padova - Dip. Mat. Pura e Appl.)
"Analytic and algebraic varieties: the classical and the non archimedean case"

-Abstract
The complex line, as a set of points, can be endowed with an analytic structure, as well as with an algebraic one. The choice of the topology and the related natural definition of functions on the space determine different geometric behaviors: in the example of the line, there are differential equations admitting solutions in both cases, and some that can be solved only in the analytic setting.
The first part of the talk will focus on the algebraic and analytic structures of a variety over the field of complex numbers, while in the second part we will give an overview of the analogous constructions for varieties defined over a non archimedean field, touching the theory of rigid analytic spaces and its relation to the study of varieties over a discrete valuation ring of mixed characteristic in the framework of syntomic cohomology.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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