Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some mod $p$ representations of quaternion algebra over
  $\mathbb{Q}_p$   Let $F$ be a totally real field in which $p$ is unramified and $B$ be a
quaternion algebra which splits at at most one infinite place. Let
$\overline{r}:\mathrm{Gal}(\overline{F}/F)\to
\mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a modular Galois representation
which satisfies the Taylor-Wiles hypotheses. Assume that for some fixed place
$v|p$, $B$ ramifies at $v$ and $F_v$ is isomorphic to $ \mathbb{Q}_p$ and
$\overline{r}$ is generic at $v$. We prove that the admissible smooth
representations of the quaternion algebra over $\mathbb{Q}_p$ coming from mod
$p$ cohomology of Shimura varieties associated to $B$ have Gelfand-Kirillov
dimension $1$. As an application we prove that the degree two Scholze's functor
vanishes on supersingular representations of $\mathrm{GL}_2(\mathbb{Q}_p)$. We
also prove some finer structure theorem about the image of Scholze's functor in
the reducible case.

35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph