p-adic Fourier Theory
| dc.creator | Schneider, Peter | |
| dc.creator | Teitelbaum, Jeremy | |
| dc.date | 2001-02-01 | |
| dc.date.accessioned | 2026-07-07T04:39:56Z | |
| dc.date.available | 2026-07-07T04:39:56Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0102012 | |
| dc.identifier | http://arxiv.org/abs/math/0102012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60876 | |
| dc.subject | Number Theory | |
| dc.subject | 11S31; 11S80; 14G22 | |
| dc.title | p-adic Fourier Theory | |
| dc.type | text |