Bell, Jamie;
(2025)
A note on the growth of Shain dihedral extensions.
Functiones et Approximatio Commentarii Mathematici
pp. 1-6.
10.7169/facm/250311-7-4.
(In press).
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Abstract
We provide a formula for the order of the Tate-Shafarevich group of elliptic curves over dihedral extensions of number fields of order 2n , up to 4th powers and primes dividing n. Specifically, for odd n it is equal to the order of the Tate-Shafarevich group over the quadratic subextension. A similar formula holds for even n.
| Type: | Article |
|---|---|
| Title: | A note on the growth of Shain dihedral extensions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.7169/facm/250311-7-4 |
| Publisher version: | https://doi.org/10.7169/facm/250311-7-4 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10215609 |
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