论文标题
Gelfand-Kirillov维度和Mod P Coomomology for GL2
Gelfand-Kirillov dimension and mod p cohomology for GL2
论文作者
论文摘要
让$ p $为质量数字，$ f $一个完全真实的数字字段在$ p $以上的地方和$ d $ $ d $的中心代数$ f $在$ p $以上的地方分配，并且在不超过一个无限位置。令$ v $是$ f $ $ p $上方的固定位置，$ \ edlline {r}：{\ rm gal}（\ edline f/f）足够通用（并在其他一些有限的地方满足某些弱的通用条件）。 We prove that many of the admissible smooth representations of $\mathrm{GL}_2(F_v)$ over $\overline{\mathbb{F}}_p$ associated to $\overline{r}$ in the corresponding Hecke-eigenspaces of the mod $p$ cohomology have Gelfand--Kirillov dimension $ [F_V：\ Mathbb {Q}] $，以及几个相关的结果。
Let $p$ be a prime number, $F$ a totally real number field unramified at places above $p$ and $D$ a quaternion algebra of center $F$ split at places above $p$ and at no more than one infinite place. Let $v$ be a fixed place of $F$ above $p$ and $\overline{r} : {\rm Gal}(\overline F/F)\rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ an irreducible modular continuous Galois representation which, at the place $v$, is semisimple and sufficiently generic (and satisfies some weak genericity conditions at a few other finite places). We prove that many of the admissible smooth representations of $\mathrm{GL}_2(F_v)$ over $\overline{\mathbb{F}}_p$ associated to $\overline{r}$ in the corresponding Hecke-eigenspaces of the mod $p$ cohomology have Gelfand--Kirillov dimension $[F_v:\mathbb{Q}]$, as well as several related results.
