Modular representations of \(\text{GL}(3,\mathbb{F}_p)\), symmetric squares, and mod-\(p\) cohomology of \(\text{GL}(3,\mathbb{Z})\) (Q1969360)
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scientific article; zbMATH DE number 1416172
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Modular representations of \(\text{GL}(3,\mathbb{F}_p)\), symmetric squares, and mod-\(p\) cohomology of \(\text{GL}(3,\mathbb{Z})\) |
scientific article; zbMATH DE number 1416172 |
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Modular representations of \(\text{GL}(3,\mathbb{F}_p)\), symmetric squares, and mod-\(p\) cohomology of \(\text{GL}(3,\mathbb{Z})\) (English)
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7 June 2000
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The authors show certain cases of nonabelian reciprocity between mod \(p\) Galois representations and Hecke eigenclasses in the mod \(p\) cohomology of \(\text{GL}(3,\mathbb{Z})\), using the symmetric square liftings from \(\text{GL}(2)\) and congruences on Hecke eigenvalues. In order to finish their proof, they develop some modular representation theory for \(\text{GL}(3,\mathbb{Z}/p)\), and invoke certain computer calculations.
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Galois representations
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mod-\(p\) cohomology
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