Bilinear forms of dimension less than or equal to 5 and function fields of quadrics in characteristic 2

2013 ◽  
Vol 286 (11-12) ◽  
pp. 1180-1190 ◽  
Author(s):  
Ahmed Laghribi ◽  
Ulf Rehmann
Keyword(s):  
Function Fields ◽  
Bilinear Forms ◽  
Characteristic 2 ◽  
And Function

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 Pinchuk maps and function fields

2014 ◽  
Vol 218 (2) ◽  
pp. 297-302
Author(s):  
L. Andrew Campbell
Keyword(s):  
Function Fields ◽  
And Function

Decomposition of Witt Rings

1982 ◽  
Vol 34 (6) ◽  
pp. 1276-1302 ◽  
Author(s):  
Andrew B. Carson ◽  
Murray A. Marshall
Keyword(s):  
Quadratic Forms ◽  
Classification Problem ◽  
Bilinear Forms ◽  
Interesting Problem ◽  
Witt Ring ◽  
Witt Rings ◽  
Finite Case ◽  
Characteristic 2 ◽  
Definition Of

We take the definition of a Witt ring to be that given in [13], i.e., it is what is called a strongly representational Witt ring in [8]. The classical example is obtained by considering quadratic forms over a field of characteristic ≠ 2 [17], but Witt rings also arise in studying quadratic forms or symmetric bilinear forms over more general types of rings [5,7, 8, 9]. An interesting problem in the theory is that of classifying Witt rings in case the associated group G is finite. The reduced case, i.e., the case where the nilradical is trivial, is better understood. In particular, the above classification problem is completely solved in this case [4, 12, or 13, Corollary 6.25]. Thus, the emphasis here is on the non-reduced case. Although some of the results given here do not require |G| < ∞, they do require some finiteness assumption. Certainly, the main goal here is to understand the finite case, and in this sense this paper is a continuation of work started by the second author in [13, Chapter 5].

On a certain analogy between algebraic number fields and function fields

2001 ◽  
pp. 512-515
Author(s):  
Ichiro Satake ◽  
Genjiro Fujisaki ◽  
Kazuya Kato ◽  
Masato Kurihara ◽  
Shoichi Nakajima
Keyword(s):  
Algebraic Number ◽  
Function Fields ◽  
Number Fields ◽  
Algebraic Number Fields ◽  
And Function
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