AresultduetoR.Greenberggivesarelationbetweenthe cardinalityof Selmergroupsof ellipticcurvesovernumberfieldsand thecharacteristicpowerseriesofPontryagindualsofSelmergroupsover cyclotomicZp-extensionsatgoodordinaryprimesp.WeextendGreenberg’sresulttomoregeneralp-adicGaloisrepresentations, includinga largesubclassof thoseattachedtop-ordinarymodular formsofweight at least4andlevelΓ0(N)withp N.
On Bloch-Kato Selmer groups and Iwasawa theory of p-adic Galois representations
Vigni, Stefano
2021-01-01
Abstract
AresultduetoR.Greenberggivesarelationbetweenthe cardinalityof Selmergroupsof ellipticcurvesovernumberfieldsand thecharacteristicpowerseriesofPontryagindualsofSelmergroupsover cyclotomicZp-extensionsatgoodordinaryprimesp.WeextendGreenberg’sresulttomoregeneralp-adicGaloisrepresentations, includinga largesubclassof thoseattachedtop-ordinarymodular formsofweight at least4andlevelΓ0(N)withp N.
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