# Tagged Questions

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Let $p$ be a prime number, $m,n \in \mathbb{N}$, $F = F(p,m)$ be the free pro-$p$ group on $m$ generators. For which $(m,n)$ there is a continuous faithful representation (embedding) $\rho : F ... 3answers 525 views ### What is the intuition behind the definition of cuspidal representations? Let$\mathbb{G}$be a reductive group defined over a number field$K$, let$Z$be its center, and let$\mathbb{A}:=\mathbb{A}_K$be the ring of adeles of$K$. Reasonably, we care about the ... 1answer 241 views ### Extended Deformation Theory (dg-Lie algebra principle in positive characteristic?) Recently, I looked at articles that make use of Deligne's idea that "in characteristic 0 every deformation problem is governed by a differential graded Lie algebra" as explained first in ... 1answer 202 views ### What is “special” maximal compact subgroup of algebraig group over local field? Learning the theory of Langlands correspondence, I met the notion of "special" maximal compact subgroup of a (reductive) algebraic group over a local field. Here, I think the word "compact" is used ... 1answer 371 views ### Explicit calculation of Weil Deligne representations According to Grothendieck monodromy theorem, l-adic galois representations of a local field corresponds to Weil-Deligne representations. However, given a galois representation, it is usually difficult ... 1answer 214 views ### Is there a semisimple$\mathbf{Q}_\ell$-representation of$G_F$ramified at an infinite set of places? See http://math.uni.lu/~wiese/galois/Boeckle-Luxemburg-Notes.pdf, Theorem 1.4(a): Is there an example of a semisimple$\mathbf{Q}_\ell$-representation$V$of$G_F$($F$a global field) ramified at a ... 1answer 279 views ### What is an automorphic representation of CM type ? In a recent paper of BL-Gee-Geraghty: "Sato-Tate for Hilbert modular forms" (JAMS 2011), a theorem is proved for regular algebrai cuspidal automorphic representation of$GL_2(\mathbb A_F)$with$F$a ... 2answers 1k views ### “Purely local” proof of local Langlands As from this website http://math.uchicago.edu/~lxiao/workshop_site/ My question is: What does it mean by "purely local"? Also, I heard about this phrase "purely local" in other problems as well, ... 3answers 1k views ### Geometric construction of depth zero local Langlands correspondence Dear community, In light of the recent work of DeBacker/Reeder on the depth zero local Langlands correspondence, I was wondering if there is an attempt to "geometrize" the depth zero local Langlands ... 0answers 437 views ### An analogue of Deligne-Lusztig theory for positive depth representations? Deligne-Lusztig theory is an important tool in understanding the depth zero representations of$p$-adic groups. Is there an analogue of Deligne-Lusztig theory that helps in understanding positive ... 1answer 550 views ### local to global Galois representation Let$\rho_p : \mbox{Gal}(\overline{\mathbb{Q}}_p / {\mathbb{Q}_p}) \to \mbox{GL}_n(\mathbb{Q}_p)$be a de Rham$p$-adic representation. Can one find a representation$\rho : ...
This question is inspired by an earlier one about the possibility of using the full ring of differential operators on a flag variety to develop a theory of localization in characteristic $p$. (Here ...