P-Adic Nevanlinna Theory Outside of a Hole

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...

P-adic Nori Theory

Given a fixed integer n, we consider closed subgroups G of GLn(Zp), where p is sufficiently large in terms of n. Assuming that the Zariski closure of G in GLn has no toric part, we give a condition on the (mod p) reduction of G which guarantees that G is of bounded index in GLn(Zp) ∩ G(Qp). In [No], Nori considered a special class of subgroups of GLn(Fp), namely groups which are generated by el...

p-Adic Fourier Theory

In this paper we generalize work of Amice and Lazard from the early sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the open unit disk over Cp. Lazard showed that this ring has a divisor theory and that the classes of closed, finitely generated, and principal ideals in this ring coincide. W...

1 p - adic Fourier theory

In the early sixties, Amice ([Am1], [Am2]) studied the space of K-valued, locally analytic functions on Z Z p and formulated a complete description of its dual, the ring of K-valued, locally Q p-analytic distributions on Z Z p , when K is a complete subfield of C p. She found an isomorphism between the ring of distributions and the space of global functions on a rigid variety over K parameteriz...