کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4584364 | 1630482 | 2015 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On completely faithful Selmer groups of elliptic curves and Hida deformations
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
In this paper, we study completely faithful torsion ZpãGã-modules with applications to the study of Selmer groups. Namely, if G is a nonabelian group belonging to certain classes of polycyclic pro-p group, we establish the abundance of faithful torsion ZpãGã-modules, i.e., non-trivial torsion modules whose global annihilator ideal is zero. We then show that such ZpãGã-modules occur naturally in arithmetic, namely in the form of Selmer groups of elliptic curves and Selmer groups of Hida deformations. It is interesting to note that faithful Selmer groups of Hida deformations do not seem to have appeared in literature before. We will also show that faithful Selmer groups have various arithmetic properties. Namely, we show that faithfulness is an isogeny invariant, and we will prove “control theorem” results on the faithfulness of Selmer groups over a general strongly admissible p-adic Lie extension.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 432, 15 June 2015, Pages 72-90
Journal: Journal of Algebra - Volume 432, 15 June 2015, Pages 72-90
نویسندگان
Meng Fai Lim,