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SUMMARY:Darmon points for number fields of mixed signature - Marc Masdeu (
 Warwick)
DTSTART:20140513T151500Z
DTEND:20140513T161500Z
UID:TALK51176@talks.cam.ac.uk
CONTACT:James Newton
DESCRIPTION:Fifteen years ago Henri Darmon introduced a construction of p-
 adic points on elliptic curves. These points were conjectured to be algebr
 aic and to behave much like Heegner points\, although so far a proof remai
 ns inaccessible. Other constructions emerged in the subsequent years\, tha
 nks to work of himself as well as Adam Logan\, Matthew Greenberg\, Mak Tri
 fkovic and Jerome Gartner\, among others. Some of these constructions were
  also non-archimedean\, but others construct points which a priori are def
 ined over the complex numbers. So far none of these constructions are know
 n to yield algebraic points\, although there is an extensive and beautiful
  collection of numerical evidence.\n\nIn this talk I will present joint wo
 rk with Xavier Guitart and Haluk Sengun\, in which we propose a framework 
 that includes all the above constructions as particular cases\, and which 
 allows us to extend the construction of local points to elliptic curves de
 fined over arbitrary number fields. I will explain our construction and pr
 esent numerical evidence supporting the new cases.
LOCATION:MR13
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