14
votes
1answer
1k views

Why is Faltings' “almost purity theorem” a purity theorem?

My understanding of purity theorems is that they come in several flavors: 1) Those of the form "this Galois representation is pure, i.e. the eigenvalues of $Frob_p$ are algebraic numbers all of whose ...
3
votes
1answer
165 views

scheme of generalizations

Hi, I have the following problem. Let $\mathcal{O}$ be a valuation ring and $S=Spec(\mathcal{O})$, denote with $s$ the closed point and with $\eta$ the generic one. Let $X\rightarrow S$ be a proper, ...
6
votes
1answer
379 views

$p$-adic uniformization not from the Drinfel'd spaces?

It seems that when we talk about the $p$-adic uniformization, we typically mean those uniformized by either the Drinfel'd upper spaces (for which we think of the examples of Mumford curves and some ...