The Lyndon–Demushkin method and crystalline lifts of G2-valued Galois representations

IF 0.9 1区数学 Q2 MATHEMATICS Algebra & Number Theory Pub Date : 2025-02-20 DOI:10.2140/ant.2025.19.415

Zhongyipan Lin

引用次数: 0

Abstract

We develop obstruction theory for lifting characteristic- $p$ local Galois representations valued in reductive groups of type $B_{l}$ , $C_{l}$ , $D_{l}$ or $G_{2}$ . An application of the Emerton–Gee stack then reduces the existence of crystalline lifts to a purely combinatorial problem when $p$ is not too small.

As a toy example, we show for all local fields $K ∕ ℚ_{p}$ , with $p > 3$ , all representations $\bar{ρ} : G_{K} \to G_{2} ({\bar{𝔽}}_{p})$ admit a crystalline lift $ρ : G_{K} \to G_{2} ({\bar{ℤ}}_{p})$ , where $G_{2}$ is the exceptional Chevalley group of type $G_{2}$ .

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

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