Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Serre weight conjectures for $p$-adic unitary groups of rank 2   We prove a version of the weight part of 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 a CM extension
of a totally real field such that every place of $F^+$ above $p$ is unramified
and inert in $F$, and let $\overline{r}: \textrm{Gal}(\overline{F^+}/F^+)
\longrightarrow {}^C\mathbf{U}_2(\overline{\mathbb{F}}_p)$ be a Galois
parameter valued in the $C$-group of a rank 2 unitary group attached to
$F/F^+$. We assume that $\overline{r}$ is semisimple and sufficiently generic
at all places above $p$. Using base change techniques and (a strengthened
version of) the Taylor-Wiles-Kisin conditions, we prove that the set of Serre
weights in which $\overline{r}$ is modular agrees with the set of Serre weights
predicted by Gee-Herzig-Savitt.

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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int