Cuspidal cohomology classes for 𝐺𝐿_{𝑛}(𝐙)

Boxer, George; Calegari, Frank; Gee, Toby

doi:10.1090/jams/1050

Cuspidal cohomology classes for $\operatorname {GL}_n(\mathbf {Z})$
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by George Boxer, Frank Calegari and Toby Gee;

J. Amer. Math. Soc.

DOI: https://doi.org/10.1090/jams/1050

Published electronically: October 11, 2024

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Abstract:

We prove the existence of a cuspidal automorphic representation $\pi$ for $\operatorname {GL}_{79}/\mathbf {Q}$ of level one and weight zero. We construct $\pi$ using symmetric power functoriality and a change of weight theorem, using Galois deformation theory. As a corollary, we construct the first known cuspidal cohomology classes in $H^*(\operatorname {GL}_{n}(\mathbf {Z}),\mathbf {C})$ for any $n > 1$.

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