Let $G = {\rm Res}_{F/\mathbb{Q}}(GL_n)$ where $F$ is a number field. Let $S^G_{K_f}$ denote an ad\`elic locally symmetric space for some level structure $K_f.$ Let ${\mathcal M}_{\mu,{\mathbb C}}$ be an algebraic irreducible representation of $G({\mathbb R})$ and we let $\widetilde{\mathcal{M}}_{\mu,{\mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data $(F,n,\mu)$ for which cuspidal cohomology of $G$ with $\mu$-coefficients, denoted $H^{\bullet}_{\rm cusp}(S^G_{K_f}, \widetilde{\mathcal{M}}_{\mu,{\mathbb C}})$, is nonzero for some $K_f.$ We prove nonvanishing of cuspidal cohomology when $F$ is a totally real field or a totally imaginary quadratic extension of a totally real field, and also for a general number field but when $\mu$ is a parallel weight.
Bhagwat, C., & Raghuram, A. (2017). Endoscopy and the cohomology of $GL(n)$. Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), 317-335.
MLA
C. Bhagwat; A. Raghuram. "Endoscopy and the cohomology of $GL(n)$". Bulletin of the Iranian Mathematical Society, 43, Issue 4 (Special Issue), 2017, 317-335.
HARVARD
Bhagwat, C., Raghuram, A. (2017). 'Endoscopy and the cohomology of $GL(n)$', Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), pp. 317-335.
VANCOUVER
Bhagwat, C., Raghuram, A. Endoscopy and the cohomology of $GL(n)$. Bulletin of the Iranian Mathematical Society, 2017; 43(Issue 4 (Special Issue)): 317-335.
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