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CATEGORIES:Number Theory Seminar
SUMMARY:Darmon points for number fields of mixed signature
- Marc Masdeu (Warwick)
DTSTART;TZID=Europe/London:20140513T161500
DTEND;TZID=Europe/London:20140513T171500
UID:TALK51176AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51176
DESCRIPTION:Fifteen years ago Henri Darmon introduced a constr
uction of p-adic points on elliptic curves. These
points were conjectured to be algebraic and to beh
ave much like Heegner points\, although so far a p
roof remains inaccessible. Other constructions eme
rged in the subsequent years\, thanks to work of h
imself as well as Adam Logan\, Matthew Greenberg\,
Mak Trifkovic and Jerome Gartner\, among others.
Some of these constructions were also non-archimed
ean\, but others construct points which a priori a
re defined over the complex numbers. So far none o
f these constructions are known to yield algebraic
points\, although there is an extensive and beaut
iful collection of numerical evidence.\n\nIn this
talk I will present joint work with Xavier Guitart
and Haluk Sengun\, in which we propose a framewor
k that includes all the above constructions as par
ticular 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 present numerical evidence s
upporting the new cases.
LOCATION:MR13
CONTACT:James Newton
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