Results 1  10
of
1,034
FROM KTHEORY TO KPOLYNOMIALS
"... The motivating problem behind this paper is understanding certain aspects of the relationship ..."
Abstract
 Add to MetaCart
The motivating problem behind this paper is understanding certain aspects of the relationship
Algebraic Ktheory of topological Ktheory
"... Let ℓp be the pcomplete connective Adams summand of topological Ktheory, with coefficient ring (ℓp) ∗ = Zp[v1], and let V (1) be the Smith–Toda complex, with BP∗(V (1)) = BP∗/(p, v1). For p ≥ 5 we explicitly compute the V (1)homotopy of the algebraic Ktheory spectrum of ℓp, denoted V (1)∗K(ℓp ..."
Abstract

Cited by 40 (16 self)
 Add to MetaCart
(ℓp). In particular we find that it is a free finitely generated module over the polynomial algebra P (v2), except for a sporadic class in degree 2p − 3. Thus also in this case algebraic Ktheory increases chromatic complexity by one. The proof uses the cyclotomic trace map from algebraic Ktheory to topological
Cyclic polytopes and the Ktheory of truncated polynomial algebras
 Inv. Math
"... This paper calculates the relative algebraic Ktheory K∗(k[x]/(xn), (x)) of a truncated polynomial algebra over a perfect field k of positive characteristic p. Since the ideal generated by x is nilpotent, we can apply McCarthy’s theorem: the relative algebraic Ktheory is isomorphic to the relative ..."
Abstract

Cited by 28 (8 self)
 Add to MetaCart
This paper calculates the relative algebraic Ktheory K∗(k[x]/(xn), (x)) of a truncated polynomial algebra over a perfect field k of positive characteristic p. Since the ideal generated by x is nilpotent, we can apply McCarthy’s theorem: the relative algebraic Ktheory is isomorphic to the relative
BASES FOR COOPERATIONS IN KTHEORY
"... Abstract. Gaussian polynomials are used to dene bases with good multiplicative properties for the algebra K(K) of cooperations in Ktheory and for the invariants under conjugation. 1. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. Gaussian polynomials are used to dene bases with good multiplicative properties for the algebra K(K) of cooperations in Ktheory and for the invariants under conjugation. 1.
On the algebraic Ktheory of the complex Ktheory spectrum
, 2006
"... Abstract. Let p � 5 be a prime, let ku be the connective complex Ktheory spectrum, and let K(ku) be the algebraic Ktheory spectrum of ku. In this paper we study the pprimary homotopy type of the spectrum K(ku) by computing its mod (p, v1) homotopy groups. We show that up to a finite summand, thes ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
Abstract. Let p � 5 be a prime, let ku be the connective complex Ktheory spectrum, and let K(ku) be the algebraic Ktheory spectrum of ku. In this paper we study the pprimary homotopy type of the spectrum K(ku) by computing its mod (p, v1) homotopy groups. We show that up to a finite summand
THE KTHEORY OF FILTERED DEFORMATIONS OF GRADED POLYNOMIAL ALGEBRAS.
"... Abstract. Recent discoveries make it possible to compute the Ktheory of certain rings from their cyclic homology and certain versions of their cdhcohomology. We extend the work of G. Cortiñas et al. who calculated the Ktheory of, in addition to many other varieties, cones over smooth varieties, ..."
Abstract
 Add to MetaCart
, or equivalently the Ktheory of homogeneous polynomial rings. We focus on specific examples of polynomial rings, which happen to be filtered deformations of homogeneous polynomial rings. Along the way, as a secondary result, we will develop a method for computing the periodic cyclic homology of a singular variety
On the Ktheory of nilpotent endomorphisms
"... In this paper, we evaluate the relative Ktheory of truncated polynomial algebras Λ = A[x]/(x n), where A is a smooth algebra over a perfect field k of positive characteristic. This extends the calculation in [3], where the basic case A = k was considered. Our ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In this paper, we evaluate the relative Ktheory of truncated polynomial algebras Λ = A[x]/(x n), where A is a smooth algebra over a perfect field k of positive characteristic. This extends the calculation in [3], where the basic case A = k was considered. Our
A LittlewoodRichardson rule for the Ktheory of Grassmannians
 Acta Math
"... Abstract. We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate Ktheory of Grassmannians to a bialgebra of stable Grothendieck polynomials, which is a Kth ..."
Abstract

Cited by 56 (2 self)
 Add to MetaCart
Abstract. We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate Ktheory of Grassmannians to a bialgebra of stable Grothendieck polynomials, which is a Ktheory
Combinatorics of the Ktheory of affine Grassmannians
, 2009
"... We introduce a family of tableaux that simultaneously generalizes the tableaux used to characterize Grothendieck polynomials and kSchur functions. We prove that the polynomials drawn from these tableaux are the affine Grothendieck polynomials and kKSchur functions – Schubert representatives for ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
for the Ktheory of affine Grassmannians and their dual in the nil Hecke ring. We prove a number of combinatorial properties including Pieri rules.
Results 1  10
of
1,034