The paper defines ordinary distributions on Rankin-Selberg eigenvarieties and proves that the Bessel period divisor controls the Selmer group divisor in one direction.
Anti-cyclotomic Euler system of diagonal cycles
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We construct split anti-cyclotomic Euler systems for Galois representations attached to certain RACSDC automorphic representations on the group $\mathrm{GL}_n\times\mathrm{GL}_{n+1}$. As a result, we make progress towards certain rank 1 cases of the Beilinson--Bloch--Kato conjecture for those representations.
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2024 1verdicts
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Bessel periods and Selmer groups over ordinary Rankin--Selberg eigenvariety
The paper defines ordinary distributions on Rankin-Selberg eigenvarieties and proves that the Bessel period divisor controls the Selmer group divisor in one direction.