تقرير
The Failure of Galois Descent for p-Selmer Groups of Elliptic Curves
| العنوان: | The Failure of Galois Descent for p-Selmer Groups of Elliptic Curves |
|---|---|
| المؤلفون: | Paterson, Ross |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11G05 (Primary) 11G07, 11N45, 14H52 (Secondary) |
| الوصف: | We show that if F is the rational numbers or a multiquadratic number field, p is 2,3, or 5, and K/F is a Galois extension of degree a power of p, then for elliptic curves E/Q ordered by height, the average dimension of the p-Selmer groups of E/K is bounded. In particular, this provides a bound for the average K-rank of elliptic curves E/Q for such K. Additionally, we give bounds for certain representation-theoretic invariants of Mordell--Weil groups over Galois extensions of such F. The central result is: for each finite Galois extension K/F of number fields and prime number p, as E/Q varies, the difference in dimension between the Galois fixed space in the p-Selmer group of E/K and the p-Selmer group of E/F has bounded average. Comment: 29 pages, main changes: improvements to bounds, height changed to naive height |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2106.02486 |
| رقم الأكسشن: | edsarx.2106.02486 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |