Timeline for Extending $p$-adic smooth and locally constant functions

4 events

when toggle format	what		by	license	comment
Jul 4 at 18:49	answer	added	LSpice		timeline score: 3
Jul 4 at 14:29	comment	added	Sentem		Yes sorry I am working with fields of characteristic $0$ and I meant $(G \cdot v)(\mathbb{Q}_p)$. I'm looking for a locally constant and smooth function $f : V \rightarrow \mathbb{C}$ whose restriction to $G \cdot v$ (which may be viewed as a function on $H \backslash G$) is the indicator function of $H \backslash H \cdot K$.
Jul 4 at 13:57	comment	added	LSpice		It's a bit unclear to me when you are working with rational points, and when not. For example, do you want to regard $X$ as $G(\mathbb Q_p)\cdot v$ or $(G\cdot v)(\mathbb Q_p)$, which can be larger? Is your $p$-adic field always of characteristic $0$, or might it be, say, $\mathbb F_p((t))$? But, most importantly, regardless of these subtleties, I don't understand the question: by almost any interpretation, $H\backslash H\cdot K$ is compact open in the analytic topology, so its indicator is already locally constant (which, to me, in this context is what smooth means). What is missing?
Jul 4 at 13:21	history	asked	Sentem	CC BY-SA 4.0