تقرير
Iwasawa theory of fine Selmer groups over global fields
| العنوان: | Iwasawa theory of fine Selmer groups over global fields |
|---|---|
| المؤلفون: | Ghosh, Sohan, Jha, Somnath, Shekhar, Sudhanshu |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11R23, 11G05, 11S25, 11R60 |
| الوصف: | The $p^\infty$-fine Selmer group of an elliptic curve $E$ over a number field $F$ is a subgroup of the classical $p^\infty$-Selmer group of $E$ over $F$. Fine Selmer group is closely related to the 1st and 2nd Iwasawa cohomology groups. Coates-Sujatha observed that the structure of the fine Selmer group of $E$ over a $p$-adic Lie extension of a number field is intricately related to some deep questions in classical Iwasawa theory; for example, Iwasawa's classical $\mu$-invariant vanishing conjecture. In this article, we study the properties of the $p^\infty$-fine Selmer group of an elliptic curve over certain $p$-adic Lie extensions of a number field. We also define and discuss $p^\infty$-fine Selmer group of an elliptic curve over function fields of characteristic $p$ and also of characteristic $\ell \neq p.$ We relate our study with a conjecture of Jannsen. Comment: 24 Pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2201.01751 |
| رقم الأكسشن: | edsarx.2201.01751 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |