Pontryagin duality for Iwasawa modules and abelian varieties
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- by King Fai Lai, Ignazio Longhi, Ki-Seng Tan and Fabien Trihan PDF
- Trans. Amer. Math. Soc. 370 (2018), 1925-1958 Request permission
Abstract:
We prove a functional equation for two projective systems of finite abelian $p$-groups, $\{\mathfrak {a}_n\}$ and $\{\mathfrak {b}_n\}$, endowed with an action of $\mathbb {Z}_p^d$ such that $\mathfrak {a}_n$ can be identified with the Pontryagin dual of $\mathfrak {b}_n$ for all $n$.
Let $K$ be a global field. Let $L$ be a $\mathbb {Z}_p^d$-extension of $K$ ($d\geq 1$), unramified outside a finite set of places. Let $A$ be an abelian variety over $K$. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of $A$.
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Additional Information
- King Fai Lai
- Affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100048, People’s Republic of China
- MR Author ID: 109300
- Email: kinglaihonkon@gmail.com
- Ignazio Longhi
- Affiliation: Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, No.111 Ren’ai Road, Suzhou Dushu Lake Higher Education Town, Suzhou Industrial Park, Jiangsu, People’s Republic of China
- Email: Ignazio.Longhi@xjtlu.edu.cn
- Ki-Seng Tan
- Affiliation: Department of Mathematics, National Taiwan University, Taipei 10764, Taiwan
- Email: tan@math.ntu.edu.tw
- Fabien Trihan
- Affiliation: Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University, 4 Yonbancho, Chiyoda-ku, Tokyo 102-0081, Japan
- MR Author ID: 637441
- Email: f-trihan-52m@sophia.ac.jp
- Received by editor(s): February 4, 2016
- Received by editor(s) in revised form: June 27, 2016
- Published electronically: August 15, 2017
- Additional Notes: The first, second, and third authors were partially supported by the National Science Council of Taiwan, grants NSC98-2115-M-110-008-MY2, NSC100-2811-M-002-079, and NSC99-2115-M-002-002-MY3, respectively
The fourth author was supported by EPSRC - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 1925-1958
- MSC (2010): Primary 11S40; Secondary 11R23, 11R34, 11R42, 11R58, 11G05, 11G10
- DOI: https://doi.org/10.1090/tran/7016
- MathSciNet review: 3739197