### Friday February
16, 2007, 1:40 PM , Goldsmith 226

**Speaker**: Jeehoon Park (BU)

**Title**: The rationality of elliptic units for real quadratic fields
over genus fields

**Abstract**:
Darmon and Dasgupta constructed elliptic units for real quadratic
fields, which is an analogue of elliptic units for imaginary
quadratic fields in the real quadratic fields and conjecturally
yields the explicit class field theory for real quadratic fields,
using *p*-adic analytic methods. Since the construction itself is
*p*-adic, we don't know apriori that the elliptic units for real
quadratic fields are global *p*-units. But they conjectured that they
are actually global *p*-units in the ring class field of real
quadratic fields. In this talk, I will explain how to prove some
special case of this conjecture, namely some linear combinations of
elliptic units are global over genus fields of real quadratic fields.
First part of my talk, I will generalize the Darmon and Dasgupta's
definition to define elliptic units attached to the modular
discriminant using Borel-Serre completion of the upper plane and
connection of elliptic units to *p*-adic family of half-integral
weight Eisenstein series. Second part of the talk, I will explain the
key ideas of the proof. The key ingredients of the proof are the
*p*-adic version of Kronecker limit formula, some factorization
formula of Dedekind zeta function of real quadratic field, and some proven
case of Gross-Stark conjecture by Gross.