Cuspidal cohomology for $GL(n)$ over a number field

A. Raghuram; Nasit Darshan

Cuspidal cohomology for $GL(n)$ over a number field

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arxiv 2407.10859 v3 pith:BCH2PGOY submitted 2024-07-15 math.NT math.RT

Nasit Darshan , A. Raghuram This is my paper · ORCID

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keywords cohomologycuspidalfieldnumberarticleborelfoundationalgalois

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abstract

The main result of this article proves the nonvanishing of cuspidal cohomology for $GL(n)$ over a number field which is Galois over its maximal totally real subfield. The proof uses the internal structure of a strongly-pure weight that can possibly support cuspidal cohomology and the foundational work of Borel, Labesse, and Schwermer.

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Betti-Whittaker periods under duality: variations and applications
math.NT 2026-07 accept novelty 7.0 of 10

For any number field F, p_ε(Π∨) ∼_{Q(Π)} G(ω_Π)^{1−n} p_ε(Π) for cohomological cuspidal GL_n(A_F), without regularity assumptions and without L-value input.

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