p-adic Fourier Theory

Details p-adic Fourier Theory p-adic Fourier Theory

2001-02-01

arxiv.org/abs/math/0102012v1

Mathematics

Number Theory

Scientific paper

In this paper we generalize work of Amice and Lazard from the early (nineteen) 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. We study the space of locally L-analytic functions on the ring of integers in L, where L is a finite extension of Qp. We show that the dual of this space is a ring isomorphic to the ring of rigid functions on a certain rigid variety X. We show that the variety X is isomorphic to the open unit disk over Cp, but not over any discretely valued extension field of L; it is a "twisted form" of the open unit disk. In the ring of functions on X, the classes of closed, finitely generated, and invertible ideals coincide, but unless L=Qp not all finitely generated ideals are principal. The paper uses Lubin-Tate theory and results on p-adic Hodge theory. We give several applications, including one to the construction of p-adic L-functions for supersingular elliptic curves.

Affiliated with

Also associated with

No associations

Rating

p-adic Fourier Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with p-adic Fourier Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and p-adic Fourier Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-203279