SEMINARIO DI MATEMATICA

giovedì 9 ottobre 2008

ore 16.00

Scuola Normale Superiore

Pisa

(Aula Mancini)

Tamás Szamuely

Istituto di Matematica Alfréd Rényi, Accademia Ungherese delle Scienze

Terrà  un seminario dal titolo:

“Grothendieck's section conjecture and zero-cycles on varieties”

Abstract

For a connected variety over a field $k$ the \'etale fundamental group of $X$ comes equipped with a projection onto the absolute Galois group of $k$. According to the widely open Section Conjecture of Grothendieck, in the case of a smooth proper curve of genus at least 2 over a number field conjugacy classes of sections of this projection should correspond to rational points on $X$.

In the first part of the lecture I shall give an introduction to the \'etale fundamental group and the Section Conjecture, and afterwards I shall present some recent results obtained jointly with D. Harari. In particular, I shall show that there exist curves for which there are sections for the projection over each completion of the number field $k$ but not over $k$.

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