FUNCTIONAL EQUATION OF CHARACTERISTIC ELEMENTS OF ABELIAN VARIETIES OVER FUNCTION FIELDS (l ≠ p)

被引：1

作者：

Pal, Aprameyo ^{[1
]}

机构：

[1] Heidelberg Univ, Math Inst, D-69120 Heidelberg, Germany

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2014年 / 10卷 / 03期

关键词：

Iwasawa theory; Selmer group; Abelian variety; function field; ELLIPTIC-CURVES; SELMER GROUPS; TORSION POINTS; ROOT NUMBERS; THEOREMS; DUALITY;

D O I：

10.1142/S1793042113501194

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we apply methods from the number field case of Perrin-Riou [20] and Zabradi [32] in the function field setup. In Z(l)- and GL(2)-cases (l not equal p), we prove algebraic functional equations of the Pontryagin dual of Selmer group which give further evidence of the main conjectures of Iwasawa theory. We also prove some parity conjectures in commutative and non-commutative cases. As a consequence, we also get results on the growth behavior of Selmer groups in commutative and non-commutative extension of function fields.

引用

页码：705 / 735

页数：31

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