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Seminario di Geometria

21 Aprile 2017, ore: 14:30
Dipartimento di Matematica e Fisica, Aula 311
Largo San Leonardo Murialdo 1 Roma

Unramified correspondences

Fedorov Bogomolov (Courant Institute, New York)

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 finite unramified covers of elliptic curves.

Per informazioni: Filippo Viviani