Serre weight conjectures for p-adic unitary groups of rank 2

نویسندگان

چکیده

We prove a version of the weight part Serre's conjecture for mod $p$ Galois representations attached to automorphic forms on rank 2 unitary groups which are non-split at $p$. More precisely, let $F/F^+$ denote CM extension totally real field such that every place $F^+$ above is unramified and inert in $F$, $\overline{r}: \textrm{Gal}(\overline{F^+}/F^+) \longrightarrow {}^C\mathbf{U}_2(\overline{\mathbb{F}}_p)$ be parameter valued $C$-group group $F/F^+$. assume $\overline{r}$ semisimple sufficiently generic all places Using base change techniques (a strengthened of) Taylor-Wiles-Kisin conditions, we set Serre weights modular agrees with predicted by Gee-Herzig-Savitt.

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ژورنال

عنوان ژورنال: Algebra & Number Theory

سال: 2022

ISSN: ['1944-7833', '1937-0652']

DOI: https://doi.org/10.2140/ant.2022.16.2005