Local-global questions on curves of genus one

Speaker: 

Felipe Voloch

Affiliation: 

University of Canterbury

Date: 

Wed, 02/11/2016 - 1:00pm

Venue: 

RC-4082, The Red Centre, UNSW

Abstract: 

We discuss a few linked questions about curves of genus one, mainly over function fields. We discuss whether a point on an elliptic curve, everywhere locally divisible by $n$, is globally divisible by $n$. We look at whether an element of the Tate-Shafarevich group of an elliptic curve is divisible by $n$ as an element of the Weil-Chatelet group and its relation with finite descent obstructions for curves of genus one. Finally, given a global point on an elliptic curve we look at obstructions for its reduction modulo a place $v$ being a generator over the residue field at $v$, for all $v$.

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