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
收藏
页码：705 / 735
页数：31
相关论文
共 50 条
  • [1] On the μ-invariants of abelian varieties over function fields of positive characteristic
    Lai, King-Fai
    Longhi, Ignazio
    Suzuki, Takashi
    Tan, Ki-Seng
    Trihan, Fabien
    ALGEBRA & NUMBER THEORY, 2021, 15 (04) : 863 - 907
  • [2] The l-parity conjecture for abelian varieties over function fields of characteristic p > 0
    Trihan, Fabien
    Yasuda, Seidai
    COMPOSITIO MATHEMATICA, 2014, 150 (04) : 507 - 522
  • [3] The Iwasawa Main Conjecture for semistable abelian varieties over function fields
    Lai, King Fai
    Longhi, Ignazio
    Tan, Ki-Seng
    Trihan, Fabien
    MATHEMATISCHE ZEITSCHRIFT, 2016, 282 (1-2) : 485 - 510
  • [4] Infinitely p-Divisible Points on Abelian Varieties Defined over Function Fields of Characteristic p > 0
    Roessler, Damian
    NOTRE DAME JOURNAL OF FORMAL LOGIC, 2013, 54 (3-4) : 579 - 589
  • [5] On the rank of abelian varieties over function fields
    Amílcar Pacheco
    manuscripta mathematica, 2005, 118 : 361 - 381
  • [6] An analogue of a conjecture of Rasmussen and Tamagawa for abelian varieties over function fields
    Melistas, Mentzelos
    INDAGATIONES MATHEMATICAE-NEW SERIES, 2024, 35 (06): : 1270 - 1281
  • [7] The Iwasawa Main Conjecture for semistable abelian varieties over function fields
    King Fai Lai
    Ignazio Longhi
    Ki-Seng Tan
    Fabien Trihan
    Mathematische Zeitschrift, 2016, 282 : 485 - 510
  • [8] On the Brauer-Siegel ratio for abelian varieties over function fields
    Ulmer, Douglas
    ALGEBRA & NUMBER THEORY, 2019, 13 (05) : 1069 - 1120
  • [9] ON THE RANK OF ABELIAN VARIETIES OVER AMPLE FIELDS
    Fehm, Arno
    Petersen, Sebastian
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (03) : 579 - 586
  • [10] The rational points on certain Abelian varieties over function fields
    Salami, Sajad
    JOURNAL OF NUMBER THEORY, 2019, 195 : 330 - 337
12345