Fundamental groups, algebraic K-theory, and a problem of Abhyankar

DOI10.1007/BF01418849zbMath0247.14005MaRDI QIDQ2555898

Mark I. Krusemeyer

Publication date: 1973

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142185

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Grothendieck groups, (K)-theory and commutative rings (13D15) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35) Curves in algebraic geometry (14H99)

Related Items (29)

Nontriviality of \(SK_ 1 (R[ M)\)] ⋮ On 2-stably isomorphic four-dimensional affine domains ⋮ Linear groups over general rings. I: Generalities. ⋮ Homologie du groupe linéaire et K-théorie de Milnor des anneaux. (Homology of the linear group and Milnor's K-theory of rings) ⋮ Excision and \(K_1\) regularity for curves with normal crossings ⋮ Polynomial extensions and excision for \(K_1\) ⋮ On invariance of the Euler class groups under a subintegral base change ⋮ The algebraic cohomotopy group and its properties ⋮ \(SK_1\) of affine curves over finite fields ⋮ On an Algebraic Analogue of the Mayer–Vietoris Sequence ⋮ 𝐾-theory of cones of smooth varieties ⋮ Affine representability results in \(\mathbb A^1\)-homotopy theory. II: Principal bundles and homogeneous spaces ⋮ The relationship between the Picard groups and \(SK_1\) of some algebraic curves ⋮ Serre's problem on projective modules over polynomial rings and algebraic K-theory ⋮ Building K-theories ⋮ Stable range for matrices ⋮ THE K-theory of some reducible affine varieties ⋮ Algebraic K-theory ⋮ K-theory of tetrahedra ⋮ \(K_2(A[X,Y/XY)\), a problem of Swan, and related computations] ⋮ Congruence subgroups and twisted cohomology of \(\text{SL}_n(F[t)\)] ⋮ The stable rank of topological algebras and a problem of R. G. Swan ⋮ The cyclic homology and 𝐾-theory of curves ⋮ The relationship between the Picard groups and \(SK_1\) of some algebraic curves ⋮ Subintegral ring extensions and some K-theoretical functors ⋮ On the homotopy groups of algebraic groups ⋮ Fields with vanishing \(K_ 2\). Torsion in \(H^ 1(X,K_ 2)\) and \(Ch^ 2(X)\) ⋮ Generators for sk₁Of plane affine curves 1 i. General facts ⋮ Generators for sk₁Of plane affine curves II. Cubic curves

Cites Work

• Variations on a theme of Chevalley
• Stable range in commutative rings
• Lectures on topics in algebraic \(K\)-theory
• Some relations between higher K-functors
• \(K\)-theory and stable algebra
• The Whitehead group of a polynomial extension
• Generators for certain ideals in regular rings of dimension three
• $K$-théorie algébrique et $K$-théorie topologique I.
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