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 hdl:20.500.11880/26361 http://dx.doi.org/10.22028/D291-26305 |
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 |
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