CRM: Centro De Giorgi
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Diophantine Geometry

course: On the structure of curves and algebraic varieties over "small" closed fields

speaker: Fedor Bogomolov (Courant Institute, New York University)

abstract: I will discuss a number of results on the structure of the image of a curve defined over $\bar Fp$ in its jacobian. Te latter is viewed as an infinite torsion group. One of the applications of these results is "rational connectedness" of all Kummer $K3$ surfaces over $\bar Fp$. Namely for any finite set of points in Kummer a $K3$ surfaces there is a chain rational curves connecting thes points. An "approximation" version of this result holds also for $\bar Q$-points for Kummer $K3$ surfaces defined over $\bar Q$.

It is a joint works with Yu.Tschinkel.

Thu 19 May, 11:00 - 12:00, Sala Conferenze Centro De Giorgi
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