scholarly journals Fat point modules over generalized Laurent polynomial rings

2007 ◽  
Vol 313 (2) ◽  
pp. 657-671
Author(s):  
Pete Goetz
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Fat Point ◽  
Point Modules

Isotriviality of torsors over Laurent polynomial rings

2005 ◽  
Vol 341 (12) ◽  
pp. 725-729 ◽  
Author(s):  
Philippe Gille ◽  
Arturo Pianzola
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings

Radicals in skew polynomial and skew Laurent polynomial rings

2014 ◽  
Vol 218 (10) ◽  
pp. 1916-1931 ◽  
Author(s):  
Chan Yong Hong ◽  
Nam Kyun Kim ◽  
Pace P. Nielsen
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Skew Polynomial

Homomorphisms of two-dimensional linear groups over Laurent polynomial rings and Gaussian domains

1991 ◽  
Vol 109 (2) ◽  
pp. 287-297 ◽  
Author(s):  
Yu Chen
Keyword(s):  
Commutative Ring ◽  
Linear Group ◽  
Unit Group ◽  
Commutative Rings ◽  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Linear Groups ◽  
Two Dimensional ◽  
Euclidean Domain ◽  
Invertible Matrices

Let GL2(R) be the general linear group of 2 × 2 invertible matrices in M2(R) over a commutative ring R with 1 and SL2(R) be the special linear group consisting of 2 × 2 matrices over R with determinant 1. In this paper we determine the homomorphisms from GL2 and SL2, as well as their projective groups, over Laurent polynomial rings to those groups over Gaussian domains, i.e. unique factorization domains (cf. Theorems 1, 2, 3 below). We also consider more generally the homomorphisms of non-projective groups over commutative rings containing a field which are generated by their units (cf. Theorems 4 and 5). So far the homomorphisms of two-dimensional linear groups over commutative rings have only been studied in some specific cases. Landin and Reiner[7] obtained the automorphisms of GL2(R), where R is a Euclidean domain generated by its units. When R is a type of generalized Euclidean domain with a degree function and with units of R and 0 forming a field, Cohn[3] described the automorphisms of GL2(R). Later, Cohn[4] applied his methods to the case of certain rings of quadratic integers. Dull[6] has considered the automorphisms of GL2(R) and SL2(R), along with their projective groups, provided that R is a GE-ring and 2 is a unit in R. McDonald [9] examined the automorphisms of GL2(R) when R has a large unit group. The most recent work of which we are aware is that of Li and Ren[8] where the automorphisms of E2(R) and GE2(R) were determined for any commutative ring R in which 2, 3 and 5 are units.

Galois cohomology and forms of algebras over Laurent polynomial rings

2007 ◽  
Vol 338 (2) ◽  
pp. 497-543 ◽  
Author(s):  
Philippe Gille ◽  
Arturo Pianzola
Keyword(s):  
Galois Cohomology ◽  
Laurent Polynomial ◽  
Polynomial Rings

scholarly journals Finite domination and Novikov rings: Laurent polynomial rings in two variables

2015 ◽  
Vol 14 (04) ◽  
pp. 1550055
Author(s):  
Thomas Hüttemann ◽  
David Quinn
Keyword(s):  
Polynomial Ring ◽  
Laurent Polynomial ◽  
Homotopy Equivalent ◽  
Polynomial Rings ◽  
Cochain Complex ◽  
Finitely Generated ◽  
Bounded Complex ◽  
Laurent Polynomial Ring ◽  
Free Modules

Let C be a bounded cochain complex of finitely generated free modules over the Laurent polynomial ring L = R[x, x-1, y, y-1]. The complex C is called R-finitely dominated if it is homotopy equivalent over R to a bounded complex of finitely generated projective R-modules. Our main result characterizes R-finitely dominated complexes in terms of Novikov cohomology: C is R-finitely dominated if and only if eight complexes derived from C are acyclic; these complexes are C ⊗L R〚x, y〛[(xy)-1] and C ⊗L R[x, x-1]〚y〛[y-1], and their variants obtained by swapping x and y, and replacing either indeterminate by its inverse.

scholarly journals Isotriviality and étale cohomology of Laurent polynomial rings

2008 ◽  
Vol 212 (4) ◽  
pp. 780-800 ◽  
Author(s):  
Philippe Gille ◽  
Arturo Pianzola
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Etale Cohomology ◽  
Étale Cohomology
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