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- W4324296817 abstract "We construct a new anticyclotomic Euler system (in the sense of Jetchev-Nekovar-Skinner) for the Galois representation $V_{f,chi}$ attached to a newform $f$ of weight $kgeq 2$ twisted by an anticyclotomic Hecke character $chi$. We then show some arithmetic applications of the constructed Euler system, including new results on the Bloch-Kato conjecture in ranks zero and one, and a divisibility towards the Iwasawa-Greenberg main conjecture for $V_{f,chi}$. In particular, in the case where the base-change of $f$ to our imaginary quadratic field has root number $+1$ and $chi$ has higher weight (which implies that the complex $L$-function $L(V_{f,chi},s)$ vanishes at the center), our results show that the Bloch-Kato Selmer group of $V_{f,chi}$ is nonzero, and if a certain distinguished class $kappa_{f,chi}$ is nonzero, then the Selmer group is one-dimensional. Such applications to the Bloch-Kato conjecture were left wide open by the earlier approaches using Heegner cycles and/or Beilinson-Flach classes. Our construction is based instead on a generalisation of the Gross-Kudla-Schoen diagonal cycles." @default.
- W4324296817 created "2023-03-16" @default.
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- W4324296817 date "2023-03-12" @default.
- W4324296817 modified "2023-09-27" @default.
- W4324296817 title "Diagonal cycles and anticyclotomic Iwasawa theory of modular forms" @default.
- W4324296817 doi "https://doi.org/10.48550/arxiv.2303.06751" @default.
- W4324296817 hasPublicationYear "2023" @default.
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