A p-adic Maass–Shimura operator on Mumford curves

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to p-adic number fields. As an application , we show how strings over a finite alphabet can be encoded in cyclotomic extensions of Qp and discuss p-adic DNA encoding. The application leads to fast p-adic agglomerative hierarchic algorithms similar to the ones recently used e....

A THEORY OF ORDINARY P-ADIC CURVES A Theory of Ordinary p-adic Curves

On Saltman’s p-adic Curves Papers

These notes are based on Saltman’s seminal work on the Brauer group Br(K) of the function field K of a p-adic curve XQp . In [S1] and [S2], Saltman showed the index of an element in the prime-to-p part of Br(K) divides the square of its period, and that all division algebras of prime degree q 6= p are cyclic. He also gave a geometric criterion for a class of prime period q 6= p to have index q....

CYCLIC COVERINGS OF THE p-ADIC PROJECTIVE LINE BY MUMFORD CURVES

Exact bounds for the positions of the branch points for cyclic coverings of the p-adic projective line by Mumford curves are calculated in two ways. Firstly, by using Fumiharu Kato’s ∗-trees, and secondly by giving explicit matrix representations of the Schottky groups corresponding to the Mumford curves above the projective line through combinatorial group theory.

p-ADIC UNIFORMIZATION OF CURVES

Let us presume that we have at our disposal the fully-formed theory of rigidanalytic spaces., as sketched in my last talk. Why would we care to look for uniformizations of algebraic objects in the rigid analytic category? Let’s look at the analogous situation in the complex-analytic category. We know that, for example, abelian varieties are uniformized by spaces of the form C/Λ, where Λ is a fr...