### Stark-Heegner/Darmon points on elliptic curves over totally real fields

- Series
- Algebra Seminar
- Time
- Monday, April 15, 2013 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Amod Agashe – Florida State University – agashe@math.fsu.edu

The classical theory of complex multiplication predicts the
existence of certain points called Heegner points defined over quadratic
imaginary fields on elliptic curves (the curves themselves are defined over
the rational numbers). Henri Darmon observed that under certain conditions, the Birch
and Swinnerton-Dyer conjecture predicts the existence of points of infinite order defined over real quadratic
fields on elliptic curves, and under such conditions, came up with a
conjectural construction of such points, which he called Stark-Heegner
points. Later, he and others (especially Greenberg and Gartner) extended
this construction to many other number fields, and the points constructed
have often been called Darmon points. We will outline a general
construction of Stark-Heegner/Darmon points defined over quadratic
extensions of totally real fields (subject to some mild restrictions) that
combines past constructions; this is joint work with Mak Trifkovic.