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 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 over global fields

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

ON THE LOCAL LANGLANDS CORRESPONDENCE FOR SPLIT CLASSICAL GROUPS OVER LOCAL FUNCTION FIELDS

2015 ◽  
Vol 16 (5) ◽  
pp. 987-1074 ◽  
Author(s):  
Radhika Ganapathy ◽  
Sandeep Varma
Keyword(s):  
Representation Theory ◽  
Function Fields ◽  
Local Fields ◽  
Linear Groups ◽  
Classical Groups ◽  
Local Function ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Residue Characteristic ◽  
Local Langlands Correspondence

We prove certain depth bounds for Arthur’s endoscopic transfer of representations from classical groups to the corresponding general linear groups over local fields of characteristic 0, with some restrictions on the residue characteristic. We then use these results and the method of Deligne and Kazhdan of studying representation theory over close local fields to obtain, under some restrictions on the characteristic, the local Langlands correspondence for split classical groups over local function fields from the corresponding result of Arthur in characteristic 0.

scholarly journals Remarks on Diophantine approximation in function fields

2019 ◽  
Vol 124 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Arijit Ganguly ◽  
Anish Ghosh
Keyword(s):  
Diophantine Approximation ◽  
Positive Characteristic ◽  
Function Fields ◽  
Local Fields ◽  
Metric Diophantine Approximation

We study some problems in metric Diophantine approximation over local fields of positive characteristic.

Local Fields

1986 ◽  
Author(s):  
J. W. S. Cassels
Keyword(s):  
Local Fields
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