Function fields of algebraic tori revisited

2017 ◽  
Vol 21 (2) ◽  
pp. 197-224 ◽  
Author(s):  
Shizuo Endo ◽  
Ming-Chang Kang
Keyword(s):  
Function Fields ◽  
Algebraic Tori

scholarly journals Finiteness theorems for algebraic tori over function fields

2021 ◽  
Vol 359 (8) ◽  
pp. 939-944
Author(s):  
Andrei S. Rapinchuk ◽  
Igor A. Rapinchuk
Keyword(s):  
Function Fields ◽  
Algebraic Tori ◽  
Finiteness Theorems

scholarly journals On a classification of the function fields of algebraic tori

1975 ◽  
Vol 56 ◽  
pp. 85-104 ◽  
Author(s):  
Shizuo Endo ◽  
Takehiko Miyata
Keyword(s):  
Finite Group ◽  
Equivalence Relation ◽  
Galois Extension ◽  
Function Fields ◽  
Equivalence Classes ◽  
Finitely Generated ◽  
Abelian Semigroup ◽  
Algebraic Tori ◽  
A Finite Group

Let II be a finite group and denote by MII the class of all (finitely generated Z-free) II-modules. In the previous paper [3] we defined an equivalence relation in MII and constructed the abelian semigroup T(II) by giving an addition to the set of all equivalence classes in MII. The investigation of the semigroup T(II) seems interesting and important, because this gives a classification of the function fields of algebraic tori defined over a field k which split over a Galois extension of k with group II.

scholarly journals ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

2020 ◽  
pp. 1-10
Author(s):  
CLEMENS FUCHS ◽  
SEBASTIAN HEINTZE
Keyword(s):  
Number Field ◽  
Function Field ◽  
Function Fields ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Linear Recurrences ◽  
Field Case ◽  
Power Sum ◽  
Linear Recurrence Sequence

Abstract Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

On geometric Z p -extensions of function fields

1988 ◽  
Vol 62 (2) ◽  
pp. 145-161 ◽  
Author(s):  
R. Gold ◽  
H. Kisilevsky
Keyword(s):  
Function Fields

scholarly journals Correction to: Divisibility problems for function fields

2020 ◽  
Vol 160 (2) ◽  
pp. 519-521
Author(s):  
S. Baier ◽  
A. Bansal ◽  
R. K. Singh
Keyword(s):  
Function Fields
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