scholarly journals Separable extensions of orthogonal involutions in characteristic two

2018 ◽  
Vol 501 ◽  
pp. 44-50 ◽  
Author(s):  
A.-H. Nokhodkar
Keyword(s):  
Characteristic Two ◽  
Separable Extensions

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

scholarly journals On class number relations in characteristic two

2007 ◽  
Vol 259 (1) ◽  
pp. 197-216 ◽  
Author(s):  
Yen-Mei J. Chen ◽  
Jing Yu
Keyword(s):  
Class Number ◽  
Characteristic Two

scholarly journals Geometric Weil representation in characteristic two

2011 ◽  
Vol 11 (2) ◽  
pp. 221-271 ◽  
Author(s):  
Alain Genestier ◽  
Sergey Lysenko
Keyword(s):  
Weil Representation ◽  
Closed Field ◽  
Triangulated Category ◽  
Algebraically Closed Field ◽  
Witt Vectors ◽  
Suitable Sense ◽  
Characteristic Two ◽  
Greenberg Realization ◽  
Geometric Analogue

AbstractLet k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack Ĝ over k, the metaplectic extension of the Greenberg realization of $\operatorname{\mathbb{S}p}_{2n}(R)$. We also construct a geometric analogue of the Weil representation of Ĝ, this is a triangulated category on which Ĝ acts by functors. This triangulated category and the action are geometric in a suitable sense.

scholarly journals FINITE GROUPS AS GALOIS GROUPS OF FUNCTION FIELDS WITH INFINITE FIELD OF CONSTANTS

2010 ◽  
Vol 88 (3) ◽  
pp. 301-312
Author(s):  
C. ÁLVAREZ-GARCÍA ◽  
G. VILLA-SALVADOR
Keyword(s):  
Finite Groups ◽  
Function Field ◽  
Function Fields ◽  
Galois Groups ◽  
Infinite Field ◽  
Separable Extension ◽  
Separable Extensions

AbstractLetE/kbe a function field over an infinite field of constants. Assume thatE/k(x) is a separable extension of degree greater than one such that there exists a place of degree one ofk(x) ramified inE. LetK/kbe a function field. We prove that there exist infinitely many nonisomorphic separable extensionsL/Ksuch that [L:K]=[E:k(x)] andAutkL=AutKL≅Autk(x)E.

scholarly journals On H-separable extensions of QF-3 rings

2003 ◽  
Vol 32 (2) ◽  
pp. 335-344
Author(s):  
Kozo SUGANO
Keyword(s):  
Separable Extensions

Isotropy of orthogonal involutions in characteristic two

2018 ◽  
Vol 17 (12) ◽  
pp. 1850240 ◽  
Author(s):  
A.-H. Nokhodkar
Keyword(s):  
Quadratic Form ◽  
Central Simple Algebra ◽  
Simple Algebra ◽  
Characteristic Two ◽  
Central Simple ◽  
The Given

A totally singular quadratic form is associated to any central simple algebra with orthogonal involution in characteristic two. It is shown that the given involution is isotropic if and only if its corresponding quadratic form is isotropic.

scholarly journals Solving quadratic equations over polynomial rings of characteristic two

1998 ◽  
Vol 42 ◽  
pp. 131-142 ◽  
Author(s):  
J. Cherly ◽  
L. Gallardo ◽  
L. Vaserstein ◽  
E. Wheland
Keyword(s):  
Polynomial Rings ◽  
Quadratic Equations ◽  
Characteristic Two
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