MIT Number Theory Seminar
Tuesday, November 07, 2017 at 4:30pm to 5:30pm
2-143
Kazim Buyukboduk (UC Dublin & Koc-Istanbul)
Title: “Iwasawa theory of modular forms over imaginary quadratic fields at $p$-non-ordinary primes”
Abstract: 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 the family of p-stabilized (unbounded) Beilinson-Flach classes, much in the spirit of Kobayashi and Pollack, which yields an Euler system (a collection of bounded cohomology classes) for the associated 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.)
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