Crystalline lifts and a variant of the Steinberg-Winter theorem (Q2695711)
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scientific article; zbMATH DE number 7671245
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Crystalline lifts and a variant of the Steinberg-Winter theorem |
scientific article; zbMATH DE number 7671245 |
Statements
Crystalline lifts and a variant of the Steinberg-Winter theorem (English)
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3 April 2023
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Summary: Let \(K/\mathbb{Q}_p\) be a finite extension. For all irreducible representations \(\bar\rho:G_K\to G(\bar{\mathbb{F}}_p)\) valued in a general reductive group \(G\), we construct crystalline lifts of \(\bar{\rho}\) which are Hodge-Tate regular. We also discuss rationality questions. We prove a variant of the Steinberg-Winter theorem along the way.
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Galois representations
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\(G\)-complete reducibility
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