The full four-step Eichler-Shimura decomposition for GSp4 is interpolated along p-adic weight families, and near any nice-enough eigenvariety point it splits with Hodge-Tate-Sen weights (-3, κ2-2, κ1-1, κ1+κ2).
On the Bloch--Kato conjecture for GSp(4) x GL(2)
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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 \'etale cohomology.
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2025 1verdicts
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Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$
The full four-step Eichler-Shimura decomposition for GSp4 is interpolated along p-adic weight families, and near any nice-enough eigenvariety point it splits with Hodge-Tate-Sen weights (-3, κ2-2, κ1-1, κ1+κ2).