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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. 30 (2021), 205-252
Published electronically: June 12, 2020
MathSciNet review: 4233182
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Abstract | References | Additional Information

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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Additional Information

Toni Annala
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T1Z2, Canada

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.