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On the structure of anticyclotomic Selmer groups of modular forms

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

赵洛晨

时间

2025年04月03日 10:00 至 11:00

地点

Shuangqing-C654

摘要

I will report the recent work with Antonio Lei and Luca Mastella, in which we determine the structure of the Selmer group of a modular form over the anticyclotomic Zp extension, assuming the imaginary quadratic field satisfies the Heegner hypothesis, that p splits in it and at which the form has good reduction, and that the bottom generalized Heegner class is primitive. Here the last assumption springs from Gross's treatment of Kolyvagin's bound on Shafarevich--Tate groups, and was put in the Iwasawa theoretic context by Matar--Nekovář and Matar for elliptic curves. I will explain our use of the vanishing of BDP Selmer groups in proving the result, which allows us to treat both ordinary/supersingular reduction types uniformly.