Please use this identifier to cite or link to this item: doi:10.22028/D291-26305
Title: On the tate modules of elliptic curves over a local field of characteristic two
Author(s): Frieden, Jochen
Language: English
Year of Publication: 2004
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: Let K:=\mathbb{F}_{2^{f}}((T)) be the field of Laurent series over the finite field with 2^{f} elements. Every non-supersingular elliptic curve \mathcal{E} over K has a short Weierstraß form Y^{2}+XY=X^{3}+\alpha X^{2}+\beta with appropriate \alpha,\beta\in K. The Tate module of \mathcal{E} yields a two dimensional representation \pi'_{\alpha,\beta} of the Weil-Deligne group W'(K^{sep}/K). Contrary to characteristics different from two, arbitrarily high ramification may occur. If \beta is integral, the rational points of \mathcal{E} can be completely described in terms of periodic functions. As a consequence, \pi'_{\alpha,\beta} is completely known. We will deal with the case in which \beta is not integral. In this case we can consider \pi'_{\alpha,\beta} as a representation \pi_{\alpha,\beta} of the Weil group W(K^{sep}/K) of K. The aim of this article is to give an explicit description of \pi_{\alpha,\beta} and to determine the ramification properties. As a consequence, we will be able to calculate the conductor.
Link to this record: urn:nbn:de:bsz:291-scidok-44928
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 127
Date of registration: 15-Feb-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

Files for this record:
File Description SizeFormat 
preprint_127_04.pdf173,67 kBAdobe PDFView/Open

Items in SciDok are protected by copyright, with all rights reserved, unless otherwise indicated.