Localizations of Grothendieck groups and Galois structure

1999 ◽  
pp. 47-63
Author(s):  
Ted Chinburg ◽  
Boas Erez ◽  
Georgios Pappas ◽  
Martin Taylor
Keyword(s):  
Galois Structure ◽  
Grothendieck Groups

scholarly journals Induced resolutions and grothendieck groups of polycyclic-by-finite-groups

1988 ◽  
Vol 53 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
Kenneth A. Brown ◽  
James Howie ◽  
Martin Lorenz
Keyword(s):  
Finite Groups ◽  
Grothendieck Groups

scholarly journals Perverse Schobers and Wall Crossing

2017 ◽  
Vol 2019 (18) ◽  
pp. 5777-5810 ◽  
Author(s):  
W Donovan
Keyword(s):  
Invariant Theory ◽  
Local System ◽  
Vector Spaces ◽  
Geometric Invariant ◽  
Perverse Sheaf ◽  
Derived Equivalences ◽  
Grothendieck Groups ◽  
Wall Crossing ◽  
Git Quotient ◽  
Cohomology Complex

Abstract For a balanced wall crossing in geometric invariant theory (GIT), there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of categories on a disk, singular at a point, with half-monodromies recovering these equivalences, and with behaviour at the singular point controlled by a GIT quotient stack associated to the wall. Taking complexified Grothendieck groups gives a perverse sheaf of vector spaces: I characterize when this is an intersection cohomology complex of a local system on the punctured disk.

Tensor Products of Dimension Groups and K0 of Unit-Regular Rings

1986 ◽  
Vol 38 (3) ◽  
pp. 633-658 ◽  
Author(s):  
K. R. Goodearl ◽  
D. E. Handelman
Keyword(s):  
Regular Ring ◽  
Hausdorff Space ◽  
Tensor Products ◽  
Matrix Algebras ◽  
Dimension Group ◽  
Grothendieck Groups ◽  
Dimension Groups ◽  
Direct Limits ◽  
Finite Products ◽  
Regular Rings

We study direct limits of finite products of matrix algebras (i.e., locally matricial algebras), their ordered Grothendieck groups (K0), and their tensor products. Given a dimension group G, a general problem is to determine whether G arises as K0 of a unit-regular ring or even as K0 of a locally matricial algebra. If G is countable, this is well known to be true. Here we provide positive answers in case (a) the cardinality of G is ℵ1, or (b) G is an arbitrary infinite tensor product of the groups considered in (a), or (c) G is the group of all continuous real-valued functions on an arbitrary compact Hausdorff space. In cases (a) and (b), we show that G in fact appears as K0 of a locally matricial algebra. Result (a) is the basis for an example due to de la Harpe and Skandalis of the failure of a determinantal property in a non-separable AF C*-algebra [18, Section 3].

The Equivariant Grothendieck Groups of the Russell-Koras Threefolds

2001 ◽  
Vol 53 (1) ◽  
pp. 3-32 ◽  
Author(s):  
J. P. Bell
Keyword(s):  
Fixed Point ◽  
Tangent Space ◽  
Unique Fixed Point ◽  
Linear Action ◽  
Grothendieck Groups ◽  
Smooth Affine

AbstractThe Russell-Koras contractible threefolds are the smooth affine threefolds having a hyperbolic *-action with quotient isomorphic to the corresponding quotient of the linear action on the tangent space at the unique fixed point. Koras and Russell gave a concrete description of all such threefolds and determined many interesting properties they possess. We use this description and these properties to compute the equivariant Grothendieck groups of these threefolds. In addition, we give certain equivariant invariants of these rings.

Galois structure for abelian p-extensions of Dedekind domains

1999 ◽  
Vol 1999 (517) ◽  
pp. 51-59
Author(s):  
M. Bondarko ◽  
K. F. Lai ◽  
S. V. Vostokov
Keyword(s):  
Galois Structure ◽  
Dedekind Domains
Sign in / Sign up

Export Citation Format

Share Document