2025/05/15 by Ming-Lun Hsieh, Hsieh, Ming-Lun, Bharathwaj Palvannan +1
Mathematics · #Advanced Mathematical Identities #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2505.09975
We study congruences involving p-adic families of Hecke eigensystems of Yoshida lifts associated with two Hida families (say F,G) of elliptic cusp forms. With appropriate hypotheses, we show that if a Hida family of genus two Siegel cusp forms admits a Yoshida lift at an appropriately chosen classical specialization, then all classical specializations are Yoshida lifts. Moreover, we prove that the characteristic ideal of the non-primitive Selmer group of (a self-dual twist of) the Rankin--Selberg convolution of F and G is divisible by the congruence ideal of the Yoshida lift associated with F and G. Under an additional assumption inspired by pseudo-nullity conjectures in higher codimension Iwasawa theory, we establish the pseudo-cyclicity of the dual of the primitive Selmer group over the cyclotomic ℤp-extension.