E[subscript n]-Regularity Implies E[subscript n-1]-Regularity
Name
Tabuada_En-regularity.pdf
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256.56 KB
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Adobe PDF
Checksum (MD5)
0088b016b1070726da58c90a82444837
Author(s)
Trigo Neri Tabuada, Goncalo Jo
Date Issued
2014
Journal
Documenta Mathematica
Publisher
European Math Society
Citation
Tabuada, Goncalo. "E[subscript n]-Regularity Implies E[subscript n-1]-Regularity." Documenta Mathematica 19 (2014), 121-139.
Version
Original manuscript
Abstract
Vorst and Dayton-Weibel proved that K[subscript n]-regularity implies K[subscript n−1]-regularity. In this article 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 establish a Nisnevich descent result which is of independent interest.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://www.math.uiuc.edu/documenta/vol-19/04.pdf
