scholarly journals Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

2011 ◽  
Vol 226 (5) ◽  
pp. 4316-4337 ◽  
Author(s):  
E. Brussel ◽  
K. McKinnie ◽  
E. Tengan
Keyword(s):  
Function Fields ◽  
Division Algebras

Algebraic elements in division algebras over function fields of curves

1985 ◽  
Vol 52 (1-2) ◽  
pp. 33-45 ◽  
Author(s):  
Michel van den Bergh ◽  
Jan van Geel
Keyword(s):  
Function Fields ◽  
Division Algebras ◽  
Algebraic Elements

scholarly journals Division algebras and maximal orders for given invariants

2016 ◽  
Vol 19 (A) ◽  
pp. 178-195 ◽  
Author(s):  
Gebhard Böckle ◽  
Damián Gvirtz
Keyword(s):  
Function Fields ◽  
Maximal Order ◽  
Global Field ◽  
Division Algebras ◽  
Wild Ramification ◽  
Maximal Orders ◽  
Cyclic Algebras

Brauer classes of a global field can be represented by cyclic algebras. Effective constructions of such algebras and a maximal order therein are given for$\mathbb{F}_{q}(t)$, excluding cases of wild ramification. As part of the construction, we also obtain a new description of subfields of cyclotomic function fields.

Division algebras over rational function fields in one variable

2005 ◽  
pp. 158-180 ◽  
Author(s):  
L. H. Rowen ◽  
A. S. Sivatski ◽  
J.-P. Tignol
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Division Algebras

Existence

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Quadratic Forms ◽  
Structure Theorem ◽  
Quadratic Extension ◽  
Quadratic Space ◽  
Division Algebras ◽  
Separable Extension ◽  
Valued Fields ◽  
Quaternion Division Algebra

This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadratic extension, a tamely ramified division algebra, a ramified separable quadratic extension, and a unique unramified quaternion division algebra. The chapter also describes ramified quaternion division algebras D₁, D₂, and D₃ over K containing a common subfield E such that E/K is a ramified separable extension.

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