scholarly journals Witt equivalence of function fields over global fields

2017 ◽  
Vol 369 (11) ◽  
pp. 7861-7881 ◽  
Author(s):  
Paweł Gładki ◽  
Murray Marshall
Keyword(s):  
Function Fields ◽  
Global Fields ◽  
Witt Equivalence

scholarly journals Witt equivalence of function fields of conics

2020 ◽  
Vol 30 (1) ◽  
pp. 63-78
Author(s):  
P. Gladki ◽  
◽  
M. Marshall
Keyword(s):  
Quadratic Form ◽  
Function Fields ◽  
Local Fields ◽  
Bilinear Forms ◽  
Conic Sections ◽  
Witt Rings ◽  
Global Fields ◽  
Witt Equivalence ◽  
Form Theory ◽  
And Function

Two fields are Witt equivalent if, roughly speaking, they have the same quadratic form theory. Formally, that is to say that their Witt rings of symmetric bilinear forms are isomorphic. This equivalence is well understood only in a few rather specific classes of fields. Two such classes, namely function fields over global fields and function fields of curves over local fields, were investigated by the authors in their earlier works [5] and [6]. In the present work, which can be viewed as a sequel to the earlier papers, we discuss the previously obtained results in the specific case of function fields of conic sections, and apply them to provide a few theorems of a somewhat quantitive flavour shedding some light on the question of numbers of Witt non-equivalent classes of such fields.

scholarly journals Witt equivalence of function fields of curves over local fields

2017 ◽  
Vol 45 (11) ◽  
pp. 5002-5013
Author(s):  
Paweł Gładki ◽  
Murray Marshall
Keyword(s):  
Function Fields ◽  
Local Fields ◽  
Witt Equivalence

scholarly journals The Farey density of norm subgroups of global fields (II)

1977 ◽  
Vol 18 (1) ◽  
pp. 57-67
Author(s):  
S. D. Cohen ◽  
R. W. K. Odoni
Keyword(s):  
Algebraic Number ◽  
Function Fields ◽  
Rational Functions ◽  
Number Fields ◽  
Ground Field ◽  
Algebraic Number Fields ◽  
Global Fields ◽  
Finite Constant

In this paper we shall derive for function fields in one variable over finite constant fields results analogous to [1], where algebraic number fields were considered. The ground field P will be the set of all rational functions in a given transcendent X, with coefficients in k = GF(q), q = pr, p a prime; thus P = k(X).

scholarly journals ON LOGARITHMIC DERIVATIVES OF ZETA FUNCTIONS IN FAMILIES OF GLOBAL FIELDS

2011 ◽  
Vol 07 (08) ◽  
pp. 2139-2156 ◽  
Author(s):  
PHILIPPE LEBACQUE ◽  
ALEXEY ZYKIN
Keyword(s):  
Error Term ◽  
Function Fields ◽  
Zeta Functions ◽  
Number Fields ◽  
Global Fields ◽  
And Function ◽  
Derivatives Of ◽  
Logarithmic Derivatives ◽  
Siegel Theorem

We prove a formula for the limit of logarithmic derivatives of zeta functions in families of global fields with an explicit error term. This can be regarded as a rather far reaching generalization of the explicit Brauer–Siegel theorem both for number fields and function fields.

MILD PRO-p-GROUPS AS GALOIS GROUPS OVER GLOBAL FIELDS

2009 ◽  
Vol 05 (05) ◽  
pp. 779-795 ◽  
Author(s):  
LANDRY SALLE
Keyword(s):  
Galois Group ◽  
Cohomology Group ◽  
Function Fields ◽  
Number Fields ◽  
Galois Groups ◽  
Global Field ◽  
Global Fields ◽  
Global Principle

This paper is devoted to finding new examples of mild pro-p-groups as Galois groups over global fields, following the work of Labute ([6]). We focus on the Galois group [Formula: see text] of the maximal T-split S-ramified pro-p-extension of a global field k. We first retrieve some facts on presentations of such a group, including a study of the local-global principle for the cohomology group [Formula: see text], then we show separately in the case of function fields and in the case of number fields how it can be used to find some mild pro-p-groups.

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