scholarly journals Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields

2007 ◽  
Vol 14 (3) ◽  
pp. 453-467 ◽  
Author(s):  
Douglas Ulmer
Keyword(s):  
Function Fields ◽  
Abelian Varieties ◽  
Jacobi Sums ◽  
Towers Of Function Fields

Non-communtative Iwasawa main conjecture

2020 ◽  
Vol 16 (09) ◽  
pp. 2041-2094
Author(s):  
Malte Witte
Keyword(s):  
Functional Equation ◽  
Galois Group ◽  
Function Field ◽  
Function Fields ◽  
Abelian Varieties ◽  
Main Conjecture

We formulate and prove an analogue of the non-commutative Iwasawa Main Conjecture for [Formula: see text]-adic representations of the Galois group of a function field of characteristic [Formula: see text]. We also prove a functional equation for the resulting non-commutative [Formula: see text]-functions. As corollaries, we obtain non-commutative generalizations of the main conjecture for Picard-[Formula: see text]-motives of Greither and Popescu and a main conjecture for abelian varieties over function fields in precise analogy to the [Formula: see text] main conjecture of Coates, Fukaya, Kato, Sujatha and Venjakob.

scholarly journals The Iwasawa Main Conjecture for constant ordinary abelian varieties over function fields

2016 ◽  
Vol 112 (6) ◽  
pp. 1040-1058 ◽  
Author(s):  
King Fai Lai ◽  
Ignazio Longhi ◽  
Ki-Seng Tan ◽  
Fabien Trihan
Keyword(s):  
Function Fields ◽  
Abelian Varieties ◽  
Main Conjecture

scholarly journals Towers of function fields over finite fields corresponding to elliptic modular curves

2012 ◽  
Vol 18 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Takehiro Hasegawa ◽  
Miyoko Inuzuka ◽  
Takafumi Suzuki
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Modular Curves ◽  
Towers Of Function Fields

Cohomology of Abelian Varieties Over Function Fields

1962 ◽  
Vol 76 (2) ◽  
pp. 185 ◽  
Author(s):  
A. P. Ogg
Keyword(s):  
Function Fields ◽  
Abelian Varieties

New Optimal Tame Towers of Function Fields over Small Finite Fields

2002 ◽  
pp. 372-389 ◽  
Author(s):  
Wen-Ching W. Li ◽  
Hiren Maharaj ◽  
Henning Stichtenoth ◽  
Noam D. Elkies
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Towers Of Function Fields

scholarly journals A note on towers of function fields over finite fields

1998 ◽  
Vol 26 (11) ◽  
pp. 3737-3741 ◽  
Author(s):  
Ferruh Özbudak ◽  
Michael Thomas
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Towers Of Function Fields
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