E_n-regularity implies E_(n-1)-regularity
K-Theory and Homology
2013-12-03 v2 Algebraic Geometry
Algebraic Topology
Abstract
Vorst and latter Dayton-Weibel proved that K_n-regularity implies K_(n-1)-regularity. In this note we generalize this result from (commutative) rings to differential graded categories and from algebraic K-theory to any functor which is Morita invariant, continuous, and localizing. Moreover, we show that regularity is preserved under taking desuspensions, fibers of morphisms, direct factors, and arbitrary direct sums. As an application, we prove that the above implication also holds for schemes. Along the way, we extend Bass' fundamental theorem to this broader setting and prove a Nisnevich descent result which is of independent interest
Keywords
Cite
@article{arxiv.1212.1112,
title = {E_n-regularity implies E_(n-1)-regularity},
author = {Goncalo Tabuada},
journal= {arXiv preprint arXiv:1212.1112},
year = {2013}
}
Comments
16 pages; revised version