The 0-th stable A^1-homotopy sheaf and quadratic zero cycles

Autor:	Asok, Aravind, Haesemeyer, Christian
Rok vydání:	2011
Předmět:	Mathematics - Algebraic Geometry Mathematics - Algebraic Topology Mathematics - K-Theory and Homology 14F42 14G05 55P42
Druh dokumentu:	Working Paper
Popis:	We study the 0-th stable A^1-homotopy sheaf of a smooth proper variety over a field k assumed to be infinite, perfect and to have characteristic unequal to 2. We provide an explicit description of this sheaf in terms of the theory of (twisted) Chow-Witt groups as defined by Barge-Morel and developed by Fasel. We study the notion of rational point up to stable A^1-homotopy, defined in terms of the stable A^1-homotopy sheaf of groups mentioned above. We show that, for a smooth proper k-variety X, existence of a rational point up to stable A^1-homotopy is equivalent to existence of a 0-cycle of degree 1. Comment: 45 pages; preliminary version, comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1108.3854 Zobrazit plný text záznamu View this record from Arxiv