Localization of the K-theory of polynomial extensions

DOI10.1007/BF01420335zbMath0415.13005OpenAlexW2068171134MaRDI QIDQ599863

Ton Vorst

Publication date: 1979

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163289

zbMATH Keywords

K-theory of polynomial extensionsKn-regularitylocalization in K- theoryQuillen K-functor

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Grothendieck groups, (K)-theory and commutative rings (13D15)

Related Items (28)

\(K\)-theory of Prüfer domains ⋮ K-theory and analytic isomorphisms ⋮ On the vanishing of relative negative K-theory ⋮ \(K_ 2 \)and \(K_ 3 \)of the circle ⋮ Pic is a contracted functor ⋮ Algebraic v. Topological K-Theory: A Friendly Match ⋮ On a conjecture of Vorst ⋮ Strong shift equivalence and algebraic \(K\)-theory ⋮ On a spectral sequence for equivariant \(K\)-theory ⋮ Comparison between algebraic and topological \(K\)-theory of locally convex algebras ⋮ Relative Milnor \(K\)-theory ⋮ The nilpotence conjecture in \(K\)-theory of toric varieties ⋮ Algebraic K-theory ⋮ Global coefficient ring in the Nilpotence Conjecture ⋮ Bass' \(NK\) groups and \(cdh\)-fibrant Hochschild homology ⋮ Niveau spectral sequences on singular schemes and failure of generalized Gersten conjecture ⋮ $K$-regularity, $cdh$-fibrant Hochschild homology, and a conjecture of Vorst ⋮ Homotopy classification of Leavitt path algebras ⋮ On the negative \(K\)-theory of schemes in finite characteristic ⋮ -THEORY OF MONOID ALGEBRAS AND A QUESTION OF GUBELADZE ⋮ Towards Vorst's conjecture in positive characteristic ⋮ On the \(K\)-theory of pullbacks ⋮ The negative K-theory of normal surfaces. ⋮ \(K_ 0\) of a union of planes through the origin ⋮ Descent for the K-theory of polynomial rings ⋮ The relative \(K_ 2\) of truncated polynomial rings ⋮ Subgroups of the elementary and Steinberg groups of congruence level \(I^ 2\) ⋮ Negative K-theory of varieties with isolated singularities

Cites Work

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• Polynomial extensions and excision for \(K_1\)
• Some formulas pertaining to the K-theory of commutative groupschemes
• Algebraic K-theory and crystalline cohomology
• A presentation for \(K_2\) of split radical pairs
• \(K_2(A[X,Y/XY)\), a problem of Swan, and related computations]
• The K-theory of endomorphisms
• Higher algebraic K-theory: I
• Localisation de formes quadratiques $I$
• On the Geometric Interpretation of Seminormality
• Introduction to Algebraic K-Theory. (AM-72)

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