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A p-adic family of Saito-Kurokawa lifts for a Coleman family and the Bloch-Kato conjecture

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Speaker: 
Kenji Makiyama
Zugehörigkeit: 
Kyoto Sangyo University
Datum: 
Don, 2017-11-23 09:50 - 10:40
Location: 
MPIM Lecture Hall

We will construct a $p$-adic family of Saito-Kurokawa lifts for a Coleman family and extend the result of Agarwal and Brown on the Bloch-Kato conjecture for elliptic modular forms of low weights to higher weights. More precisely, we will prove that the $p$-valuation of the order of the Selmer group of a Coleman deformation is bounded below by the $p$-valuation of the algebraic part of the critical $L$-value attached to the initial Hecke eigenform of a Coleman family satisfying some reasonable assumptions given by Agarwal and Brown.

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