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Iwasawa Main Conjecture for Rankin-Selberg p-adic L-functions
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In this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa main conjecture for the p-adic L-function. We prove this conjecture using the congruences between Klingen Eisensteinseries and cusp forms on the group GU(3; 1), following the strategy of a recent work of C. Skinner and E. Urban. This theorem can be used to deduce a converse of Gross-Zagier-Kolyvagin theorem and the precise BSD formula in the rank one case.
Forward citations
Cited by 3 Pith papers
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A proof of Perrin-Riou's Heegner point main conjecture
The authors prove Perrin-Riou's Heegner point main conjecture for elliptic curves over the rationals under mild hypotheses, and also prove the Iwasawa-Greenberg main conjecture for Bertolini-Darmon-Prasanna p-adic L-f...
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Iwasawa theory for $\mathrm{U}(r,s)$, Bloch-Kato conjecture and Functional Equation
For ordinary automorphic forms on unitary groups U(r,s) over totally real fields, it proves that a rank-zero Selmer group forces the central L-value to be nonzero.
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On Howard's main conjecture and the Heegner point Kolyvagin system
The paper upgrades Howard's divisibility to the full Howard main conjecture when the Heegner-point Kolyvagin system is primitive, and shows the conjecture is equivalent to primitivity plus a Tamagawa-factor condition.
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