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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Thomason's theorem for varieties over algebraically closed fields


Author: Mark E. Walker
Journal: Trans. Amer. Math. Soc. 356 (2004), 2569-2648
MSC (2000): Primary 19E15, 19E20, 14F20
DOI: https://doi.org/10.1090/S0002-9947-03-03479-2
Published electronically: October 29, 2003
MathSciNet review: 2052190
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Abstract: We present a novel proof of Thomason's theorem relating Bott inverted algebraic $K$-theory with finite coefficients and étale cohomology for smooth varieties over algebraically closed ground fields. Our proof involves first introducing a new theory, which we term algebraic $K$-homology, and proving it satisfies étale descent (with finite coefficients) on the category of normal, Cohen-Macaulay varieties. Then, we prove algebraic $K$-homology and algebraic $K$-theory (each taken with finite coefficients) coincide on smooth varieties upon inverting the Bott element.


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Additional Information

Mark E. Walker
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0323
Email: mwalker@math.unl.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03479-2
Keywords: Algebraic $K$-theory, \'etale cohomology, Thomason's theorem
Received by editor(s): August 24, 2002
Published electronically: October 29, 2003
Article copyright: © Copyright 2003 American Mathematical Society