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arXiv · 2605.03519

Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fields

Jelena Ivančić·Vaughan McDonald
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Abstract

Let $p$ be a prime, and let $F$ be a CM field containing an imaginary quadratic field in which $p$ splits. We show that the locally analytic vectors of Hecke eigenspaces in the ($p$-adic) completed cohomology of $\mathrm{GL}_n/F$, localized at a non-Eisenstein decomposed generic maximal ideal, admit infinitesimal characters determined by the Sen operators of the corresponding Galois representations, thus confirming a conjecture of Dospinescu-Pa\v{s}k\={u}nas-Schraen in this case.

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Jelena Ivančić, Vaughan McDonald. 2026-05-05. Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fields. https://arxiv.org/abs/2605.03519

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