Vanishing linear periods of cuspidal automorphic sheaves for \(\mathrm{GL}_{m+n}\). (English) Zbl 07864460
Let \(X\) stand for a connected smooth projective curve over an algebraically closed field with genus greater than one. Let \(E\) stand for an irreducible local system of rank \(m + n\) over \(X\). We denote by \(\mathrm{Per}_E\) the linear period of \(\mathrm{Aut}_E\), the automorphic \(E\)-Hecke eigensheaf on the stack classifying rank \(m + n\) vector bundles on \(X\).
In the paper under the review, the author shows that if \(m \neq n\) and \(m, n \geq 1\), then all cohomology sheaves of \(\mathrm{Per}_E\) vanish.
In the paper under the review, the author shows that if \(m \neq n\) and \(m, n \geq 1\), then all cohomology sheaves of \(\mathrm{Per}_E\) vanish.
Reviewer: Ivan Matić (Osijek)
MSC:
| 11R39 | Langlands-Weil conjectures, nonabelian class field theory |
| 11S37 | Langlands-Weil conjectures, nonabelian class field theory |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 14H60 | Vector bundles on curves and their moduli |
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