A Study of the p-Adic Frobenius Lifts and p-Adic Periods, from a Deformation Theory Viewpoint

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

P-adic Superspaces and Frobenius

The notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over Z p (the ring of p-adic integers). This article partially intersects with [9]; it contains the proofs omitted in [9] as well as some investigations into the important notion of a prorepresentable p-adic superspace.

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

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

p-ADIC ARAKELOV THEORY

We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work of Colmez on p-adic Green functions. We introduce the p-adic version of a metrized line bundle and define the met...