On quadratic forms and abelian varieties over function fields

1982 ◽  
pp. 249-264 ◽  
Author(s):  
Albrecht Pfister
Keyword(s):  
Quadratic Forms ◽  
Function Fields ◽  
Abelian Varieties

scholarly journals Pencils of Quadratic Forms and Hyperelliptic Function Fields

2000 ◽  
Vol 227 (2) ◽  
pp. 532-548
Author(s):  
David B. Leep ◽  
Laura Mann Schueller
Keyword(s):  
Quadratic Forms ◽  
Function Fields ◽  
Hyperelliptic Function

Algorithms for quadratic forms over real function fields

2016 ◽  
Vol 108 ◽  
pp. 133-141
Author(s):  
Konrad Jałowiecki ◽  
Przemysław Koprowski
Keyword(s):  
Real Function ◽  
Quadratic Forms ◽  
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
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