$K$-theory of affine toric varieties

Gubeladze, Joseph

doi:10.4310/hha.1999.v1.n1.a5

Cited by 18 publications

(30 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Thus K e G (X) is a projective module over R( G). Moreover, since R( G) is a tensor product of a polynomial ring and a Laurent polynomial ring K e G (X) is in fact free over R( G) (see Theorem 1.1 of [12]). …”

Section: Preliminaries On K-theorymentioning

confidence: 99%

Equivariant K-theory of compactifications of algebraic groups

Uma

2007

Transformation Groups

View full text Add to dashboard Cite

In this article we describe the G×G-equivariant K-ring of X, where X is a regular compactification of a connected complex reductive algebraic group G. Furthermore, in the case when G is a semisimple group of adjoint type, and X its wonderful compactification, we describe its ordinary Kring K(X). More precisely, we prove that K(X) is a free module over K(G/B) of rank the cardinality of the Weyl group. We further give an explicit basis of K(X) over K(G/B), and also determine the structure constants with respect to this basis.

show abstract

Section: Preliminaries On K-theorymentioning

confidence: 99%

Equivariant K-theory of compactifications of algebraic groups

Uma

2007

Transformation Groups

View full text Add to dashboard Cite

show abstract

“…In this case, we have R ∼ = k 1 × · · · × k m , where each k i is a field. The assertion (1) now follows [15,Theorem 1.3].…”

Section: 3mentioning

confidence: 82%

“…Gubeladze proved several results on this subject in a series of many papers ( [11], [14], [15] and [16] to name a few). Using the new direction provided by [19] and [3], Cortiñas, Haesemeyer, Walker and Weibel together have made significant advances in the study of algebraic K-theory of monoid algebras (see [4], [5], [6] and [7]).…”

Section: Introductionmentioning

confidence: 93%

See 1 more Smart Citation

Negative 𝐾-theory and Chow group of monoid algebras

Krishna¹,

Sarwar²

2020

𝐾-Theory in Algebra, Analysis And Topology

View full text Add to dashboard Cite

We show, for a finitely generated partially cancellative torsion-free commutative monoid M , that K i (R) ∼ = K i (R[M ]) whenever i ≤ −d and R is a quasi-excellent Q-algebra of Krull dimension d ≥ 1. In particular, K i (R[M ]) = 0 for i < −d. This is a generalization of Weibel's K-dimension conjecture to monoid algebras. We show that this generalization fails for X[M ] if X is not an affine scheme. We also show that the Levine-Weibel Chow group of 0-cycles CH LW 0 (k[M ]) vanishes for any finitely generated commutative partially cancellative monoid M if k is an algebraically closed field. 0.1. Weibel's conjecture for monoid algebras. Recall that a famous conjecture of Weibel [36] asserts that if R is a commutative Noetherian ring of Krull dimension d, then K −d (R) ≃ K −d (R[t 1 , · · · , t n ]) and K i (R[t 1 , · · · , t n ]) = 0 for i < −d and n ≥ 0. An affirmative answer to this conjecture was obtained recently by Kerz, Strunk and Tamme [22]. For Noetherian rings containing Q, this was earlier solved by Cortiñas, Haesemeyer, Schlichting and Weibel [3] (see also [10], [23] and [38] for older results in positive characteristics).The main technical tool that goes into the proof of Weibel's conjecture in [22] is a pro-cdhdescent theorem for algebraic K-theory. However, the final step in the proof of the conjecture 2010 Mathematics Subject Classification. Primary 19D50; Secondary 13F15, 14F35.

show abstract

“…More recent results on K-regularity of rings were obtained by Gubeladze [11,12] and by Cortinas, Haesemeyer and Weibel [13]. For commutative C * -algebras the K-regularity was established by Rosenberg [14].…”

Section: Introductionmentioning

confidence: 94%

Smooth K-groups for Monoid Algebras and K-regularity

Inassaridze

2015

Mathematics

View full text Add to dashboard Cite

The isomorphism of Karoubi-Villamayor K-groups with smooth K-groups for monoid algebras over quasi stable locally convex algebras is established. We prove that the Quillen K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable Frechet algebras having a properly uniformly bounded approximate unit and not necessarily m-convex. Based on these results the K-regularity property for quasi-stable Frechet algebras having a properly uniformly bounded approximate unit is established.

show abstract

$K$-theory of affine toric varieties

Cited by 18 publications

References 17 publications

Equivariant K-theory of compactifications of algebraic groups

Equivariant K-theory of compactifications of algebraic groups

Negative 𝐾-theory and Chow group of monoid algebras

Smooth K-groups for Monoid Algebras and K-regularity

Contact Info

Product

Resources

About