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DERIVED ALGEBRAIC COBORDISM

Part of: Homology and cohomology theories (Co)homology theory Cycles and subschemes

Published online by Cambridge University Press:  30 October 2014

Parker E. Lowrey  and
Timo Schürg
Parker E. Lowrey
Affiliation:
Department of Mathematics, Middlesex College, The University of Western Ontario, London, ON, Canada (plowrey@uwo.ca)
Timo Schürg
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany (timo_schuerg@operamail.com)
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Abstract

We construct a cohomology theory using quasi-smooth derived schemes as generators and an analog of the bordism relation using derived fiber products as relations. This theory has pull-backs along all morphisms between smooth schemes independent of any characteristic assumptions. We prove that, in characteristic zero, the resulting theory agrees with algebraic cobordism as defined by Levine and Morel. We thus obtain a new set of generators and relations for algebraic cobordism.

Keywords

algebraic cobordismvirtual fundamental classesquasi-smooth schemes

MSC classification

Primary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Secondary: 14C40: Riemann-Roch theorems 55N22: Bordism and cobordism theories, formal group laws

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 2 , April 2016 , pp. 407 - 443
Copyright
© Cambridge University Press 2014 

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