A^1-homotopy invariance in spectral algebraic geometry
Algebraic Topology
2020-10-16 v2 Algebraic Geometry
K-Theory and Homology
Abstract
We study two different flavours of A^1-homotopy theory in the setting of spectral algebraic geometry, and compare them to classical A^1-homotopy theory. As an application we show that the spectral analogue of Weibel's homotopy invariant K-theory collapses to the classical theory. Along the way we give a new construction of nonconnective algebraic K-theory of stable infinity-categories via a generalization of the Bass-Thomason-Trobaugh construction.
Keywords
Cite
@article{arxiv.1705.03340,
title = {A^1-homotopy invariance in spectral algebraic geometry},
author = {Denis-Charles Cisinski and Adeel A. Khan},
journal= {arXiv preprint arXiv:1705.03340},
year = {2020}
}
Comments
47 pages; v2: completely rewritten with a new section on the Bass construction over the sphere spectrum