Projective modules over smooth, affine varieties over real closed fields

JOURNAL OF ALGEBRA

卷:323

Article

Bhatwadekar, S. M.¹  Sane, Sarang¹ 

[1] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

关键词: Projective modules;    Euler class groups;    Real closed fields;    Semialgebraically connected semialgebraic components Elementary paths;   

DOI  :  10.1016/j.jalgebra.2009.12.028

来源: Elsevier

【 摘 要 】

Let X = Spec(A) be a smooth, affine variety of dimension n >= 2 over the field R of real numbers. Let P be a projective A-module of rank n such that its nth Chern class C-n(P) is an element of CH0(X) is zero. In this set-up, Bhatwadekar-Das-Mandal showed (amongst many other results) that P similar or equal to A circle plus Q in the case that either n is odd or the topological space X(R) of real points of X does not have a compact, connected component. In this paper, we prove that similar results hold for smooth, affine varieties over an arbitrary real closed field R. The proof is algebraic and does not make use of Tarski's principle, nor of the earlier result for R. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free