witt rings
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Author(s):  
Jens Hornbostel ◽  
Heng Xie ◽  
Marcus Zibrowius
Keyword(s):  

2020 ◽  
Vol 12 (1) ◽  
pp. 1-23
Author(s):  
Pawel Gladki ◽  
Krzysztof Worytkiewicz
Keyword(s):  

2020 ◽  
Vol 30 (1) ◽  
pp. 63-78
Author(s):  
P. Gladki ◽  
◽  
M. Marshall

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.


2018 ◽  
Vol 68 (6) ◽  
pp. 1339-1342 ◽  
Author(s):  
Beata Rothkegel

Abstract The main theorem of the paper gives an example of a non-maximal order 𝓞 in a quadratic number field K such that the homomorphism W𝓞 → WK of Witt rings is injective.


2018 ◽  
Vol 499 ◽  
pp. 229-271 ◽  
Author(s):  
Tom Bachmann
Keyword(s):  

2015 ◽  
Vol 14 (3) ◽  
pp. 109-119
Author(s):  
Marcin Ryszard Stepien ◽  
Keyword(s):  

2014 ◽  
Vol 163 (1) ◽  
pp. 1-13
Author(s):  
Alfred Czogała ◽  
Mieczysław Kula
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2013 ◽  
Vol 12 (4) ◽  
pp. 119-125
Author(s):  
Marcin Ryszard Stepien ◽  
◽  
Lidia Stepien ◽  
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