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The diagonal cycle Euler system for ${\rm GL}_2\times{\rm GL}_2$

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arxiv 2106.05322 v3 pith:YCSE6FQ2 submitted 2021-06-09 math.NT

Raúl Alonso , Francesc Castella , Óscar Rivero This is my paper
classification math.NT
keywords conjecturediagonaleulersystemadicanalyticanticyclotomicapplications
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abstract

We construct an anticyclotomic Euler system for the Rankin-Selberg convolution of two modular forms, using $p$-adic families of generalized Gross-Kudla-Schoen diagonal cycles. As applications of this construction, we prove new cases of the Bloch-Kato conjecture in analytic ranks zero and one, and a divisibility towards an Iwasawa main conjecture.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Anticyclotomic diagonal classes and Beilinson--Flach elements

    math.NT 2025-09 conditional novelty 6.0 of 10

    Anticyclotomic diagonal cycle classes are shown to match Beilinson-Flach elements up to explicit factors for a CM weight-one Eisenstein degeneration.

  2. Diagonal cycles and anticyclotomic twists of modular forms at inert primes

    math.NT 2025-07 conditional novelty 6.0 of 10

    Nonvanishing of the Chida-Hsieh Heegner theta element implies one-dimensionality of the Bloch-Kato Selmer group for anticyclotomic twists of modular forms at inert primes.

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