[Turkmath:8446] Seminar of Ricardo Menares on Thursday, June 14th at MSGSU Bomonti.

[Ozer Ozturk]

Dear All,

Ricardo Menares (Pontificia Universidad Católica de Valparaíso) will give a seminar on Thursday, June 14th at 16:30 at MSGSU Bomonti Building.

Title: "Arakelov theory and Hecke correspondences on modular curves"

Abstract: In the context of arithmetic surfaces, J.-B. Bost defined a
generalised Arithmetic Chow Group (ACG) using the Sobolev space L^2_1.
We study the behaviour of these groups under pull-back and push-forward
and we prove a projection formula. We use these results to define an
action of the Hecke operators on the ACG of modular curves  and to
show that they are self-adjoint with respect to the arithmetic
intersection product.   The decomposition of the ACG in
eigencomponents which follows  allows us to define new numerical
invariants, which are refined versions of  the self-intersection of
the dualizing sheaf. Using  the Gross-Zagier formula and a calculation
due independently to Bost and Kühn we compute these invariants in
terms of special values of L series.


Sincerely,
Ozer Ozturk.