Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Bivariant derived algebraic cobordism


Author: Toni Annala
Journal: J. Algebraic Geom.
DOI: https://doi.org/10.1090/jag/754
Published electronically: June 12, 2020
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Abstract: We extend the derived algebraic bordism of Lowrey and Schürg to a bivariant theory in the sense of Fulton and MacPherson and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings of singular quasi-projective schemes. The extended cobordism is shown to specialize to algebraic $ K^0$ analogously to the Conner-Floyd theorem in topology. We also give a candidate for the correct definition of Chow rings of singular schemes.


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Toni Annala
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T1Z2, Canada
Email: tannala@math.ubc.ca

DOI: https://doi.org/10.1090/jag/754
Received by editor(s): November 25, 2018
Received by editor(s) in revised form: December 8, 2018, and August 25, 2019
Published electronically: June 12, 2020
Article copyright: © Copyright 2020 University Press, Inc.