Lombardo, Davide and Perucca, Antonella (2017) The 1-eigenspace for matrices in GL(2)(Z(l)). NEW YORK JOURNAL OF MATHEMATICS, 23. pp. 897-925. ISSN 1076-9803,
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Fix some prime number l and consider an open subgroup G either of GL(2)(Z(l)) or of the normalizer of a Cartan subgroup of GL(2)(Z(l)). The elements of G act on (Z/l(n)Z)(2) for every n >= 1 and also on the direct limit, and we call 1-eigenspace the group of fixed points. We partition G by considering the possible group structures for the 1-eigenspace and show how to evaluate with a finite procedure the Haar measure of all sets in the partition. The results apply to all elliptic curves defined over a number field, where we consider the image of the l-adic representation and the Galois action on the torsion points of order a power of l.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CURVES; Haar measure; general linear group; Cartan subgroup; l-adic representation; elliptic curve |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:01 |
| Last Modified: | 28 Feb 2019 10:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/657 |
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