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- W3136703591 abstract "Let $p$ be a prime number and $mathrm{Gal}_p$ be the Galois group of the maximal abelian extension unramified outside $pinfty$ of a totally real number field $F$ of degree $d$. Using automorphic cycles, we construct evaluation maps on the parahoric overconvergent cohomology for $mathrm{GL}_{2n}/F$ in degree $d (n^2 + n -1)$, which allow us to attach a distribution on $mathrm{Gal}_p$ of controlled growth to any finite slope overconvergent $U_p$-eigenclass. When the eigenclass comes from a non-critical refinement $tildepi$ of a cuspidal automorphic representation $pi$ of $mathrm{GL}_{2n}/F$ which is spherical at $p$ and admits a Shalika model, we prove this distribution interpolates all Deligne-critical $L$-values of $pi$, giving the first construction of $p$-adic $L$-functions in this generality beyond the $p$-ordinary setting. Further, under some mild assumptions we use our evaluation maps to show that $tildepi$ belongs to a unique $(d+1)$-dimensional Shalika family in a parabolic eigenvariety for $mathrm{GL}_{2n}/F$, and that this family is 'etale over the weight space. Finally, under a hypothesis on the local Shalika models at bad places which is empty for $pi$ of level 1, we construct a $p$-adic $L$-function for the family." @default.
- W3136703591 created "2021-03-29" @default.
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- W3136703591 date "2021-03-19" @default.
- W3136703591 modified "2023-09-27" @default.
- W3136703591 title "On $p$-adic $L$-functions for $GL_{2n}$ in finite slope Shalika families" @default.
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