A^1-connected components of schemes
Algebraic Geometry
2016-10-07 v3 K-Theory and Homology
Abstract
A conjecture of Morel asserts that the sheaf of A^1-connected components of a simplicial sheaf X is A^1-invariant. A conjecture of Asok-Morel asserts that A^1-connected components of smooth k-schemes coincide with their A^1-chain-connected components and are birational invariants of smooth proper schemes. In this article, we exhibit examples of schemes for which Asok-Morel's conjectures fail to hold and whose Sing_* is not A^1-local. We also give equivalent conditions for Morel's conjecture to hold. A method suggested by these results is then used to prove Morel's conjecture for non-uniruled surfaces over a field k.
Keywords
Cite
@article{arxiv.1312.6388,
title = {A^1-connected components of schemes},
author = {Chetan Balwe and Amit Hogadi and Anand Sawant},
journal= {arXiv preprint arXiv:1312.6388},
year = {2016}
}
Comments
24 pages; v3: Minor changes. Final version before page proofs. Accepted for publication in Advances in Mathematics