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# Seminario / Bogomolov

SEMINARIO DI GEOMETRIA ALGEBRICA

Nell'ambito del seminario congiunto di geometria algebrica organizzato dai Dipartimenti di Matematica dell'Università e del Politecnico di Milano, si terrà il seguente seminario:

il 2 maggio alle 14:30 presso la Sala di Rappresentanza
Fedor Bogomolov
(Courant Institute of Mathematical Sciences)
Unramified correspondences

Abstract :
I will report on the results of an ongoing project which we began some years ago with Yuri Tschinkel and continue with Hang Fu and Jin Qian. We say that a smooth projective curve $C$ dominates $C'$ if there is nonramified covering $\tilde C$ of $C$ which has a surjection onto $C'$. Thanks to Bely theorem we can show that any curve $C'$ defined over $\bar Q$ is dominated by one of the curves $C_n, y^n-1= x^2$. Over $\bar F_p$ any curve in fact is dominated by $C_6$ which is in way also a minimal possible curve with such a property. Conjecturally the same holds over $\bar Q$ but at the moment we can prove only partial results in this direction. There are not many methods to establish dominance for a particular pair of curves and the one we use is based on the study of torsion points and finitee unramified covers of elliptic curves.
26 aprile 2017