STNB2018 (32nd edition)
Big Heegner points and some cases of the Bloch-Kato conjecture
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Abstract
In this talk, we will explain Castellà's result on some rank 0 cases of the Bloch-Kato conjecture for twists of newforms by certain anticyclotomic Hecke characters. The strategy of the proof combines: 1) the existence of a big $p$-adic regulator map that connects the $p$-adic $L$-function introduced in the second talk with the Big Heegner point defined in the third talk, and 2) Fouquet's generalization of the Kolyvagin method seen in the first talk.
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