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On the anticyclotomic main conjectures for modular forms Büyükboduk, Kazım

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I will report on recent joint work with Antonio Lei on the anticyclotomic Iwasawa theory of the base change of an elliptic modular form to an imaginary quadratic field \(K\) in which the prime \(p\) splits. We treat both the definite and indefinite cases in both \(p\)-ordinary and non-\(p\)-ordinary situations. One of our main results is an equality (up to powers of \(p\)) that is predicted by the main conjectures in the definite \(p\)-ordinary set up and a \(\Lambda\)-adic Birch and Swinnerton-Dyer formula in the indefinite case.

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