Thomason’s theorem for varieties over algebraically closed fields
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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.References
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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
- Received by editor(s): August 24, 2002
- Published electronically: October 29, 2003
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2052190