Orbit spaces of unimodular rows over smooth real affine algebras

DOI10.1007/s00222-017-0764-yzbMath1388.13027OpenAlexW2766810899MaRDI QIDQ1745393

Soumi Tikader, Mrinal Kanti Das, Md. Ali Zinna

Publication date: 17 April 2018

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

Full work available at URL: https://doi.org/10.1007/s00222-017-0764-y

zbMATH Keywords

unimodular rowEuler class groupstably free moduleweak Mennicke symbolhomotopy orbitnaive homotopy

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Algebraic cycles (14C25) Stability for projective modules (19A13) Efficient generation of modules (19A15)

Related Items (6)

On a question of Nori: obstructions, improvements, and applications ⋮ Motivic stable cohomotopy and unimodular rows ⋮ ``\({\mathbb{P}}^1\)-gluing for local complete intersections ⋮ Equivalent generating pairs of an ideal of a commutative ring ⋮ Two lives: compositions of unimodular rows ⋮ Equivalent generating vectors of finitely generated modules over commutative rings

Cites Work

• Secondary characteristic classes and the Euler class
• Some remarks on orbit sets of unimodular rows
• Projective modules over smooth, affine varieties over real closed fields
• A group structure on certain orbit sets of unimodular rows
• Cancellation over affine varieties
• Symplectic bundles over affine surfaces
• The Bass-Quillen conjecture in dimension three but characteristic \(\neq 2,3\) via a question of A. Suslin
• A module structure on certain orbit sets of unimodular rows
• Projective generation of curves in polynomial extensions of an affine domain and a question of Nori
• On the Bass-Quillen conjecture concerning projective modules over polynomial rings
• Complete intersections
• Zero cycles and the Euler class groups of smooth real affine varieties
• Chow groups with coefficients
• Extrapolating an Euler class
• ``Strong Euler class of a stably free module of odd rank
• A nice group structure on the orbit space of unimodular rows
• Projective modules over smooth real affine varieties
• \(K\)-theory and stable algebra
• The Homotopy Obstructions in Complete Intersections
• Polynomial rings and their projective modules
• The general linear group of polynomial rings over regular rings
• SERRE'S PROBLEM ON PROJECTIVE MODULES OVER POLYNOMIAL RINGS, AND ALGEBRAIC $ K$-THEORY
• ON STABLY FREE MODULES
• Mennicke symbols, 𝐾-cohomology and a Bass-Kubota theorem
• Unnamed Item
• Unnamed Item

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