Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Kazim Buyukboduk
Affiliation:

UC Dublin/Koc University Istanbul/zur Zeit MPIM
Date:

Wed, 2017-11-15 14:15 - 15:15 We will report on our joint work with A. Lei towards the main conjectures (in one or two-variables) for the

Rankin-Selberg convolutions of the base change of a $p$-non-ordinary modular form to an imaginary quadratic

field $K$, with ray class characters of $K$. The crucial ingredient is a signed-splitting procedure for two families

of $p$-stabilized (unbounded) Beilinson-Flach classes, much in the spirit of Kobayashi and Pollack, which yields

a pair of Euler systems (collections of bounded cohomology classes) for the associated to motive. In the indefinite

anticyclotomic set up (where we show that the main conjectures themselves reduce to $0=0$), our methods also

yield a divisibility in a $\Lambda$-adic Birch and Swinnerton-Dyer formula. (These circle of ideas partially

extend to allow the treatment more general $p$-non-ordinary Rankin-Selberg products and symmetric squares;

this is joint work in progress with with A. Lei, D. Loeffler and G. Venkat.)

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246