Speaker: Đỗ Kim Tuấn (University of California, Los Angeles)
Time: 10:20 - 11:20, December 25, 2024
Venue:Â Room 612, A6, Institute of Mathematics-VAST
Abstract: Let f be a newform of weight 2k and level $Gamma_0(N)$. Let chi be an anti-cyclotomic Hecke character of K. Let V be the Galois representation attached to f twisted by chi. In this talk, I will start from the Birch--Swinnerton-Dyer conjecture and the story of Heegner points. Then I will describe the `diagonal cycle' Euler system over K for V. Here, K can represent either an imaginary quadratic field, where this case is a collaboration with F. Castella, or an imaginary biquadratic field. Arithmetic applications include results towards the Bloch--Kato Conjecture and the Iwasawa Main Conjecture for V.
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