On the Bloch--Kato conjecture for GSp(4) x GL(2)

Abstract

We prove the Bloch--Kato conjecture for certain critical values of degree 8 $L$-functions associated to cusp forms on ${\mathrm{GSp}}_4\times {\mathrm{GL}}_2$. We also construct a $p$-adic Eichler--Shimura isomorphism in Hida families for ${\mathrm{GSp}}_4$, relating $H^2$ of automorphic vector bundles with ${\mathbf{D}}_{\mathrm{cris}}$ of a subquotient of étale cohomology.

arXiv comment30 pages. v2: updated references and acknowledgements

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Cited by in corpus (2)

• On some zeta-integrals for unramified representations of GSp(4)
• On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces