Algebraic elliptic cohomology theory and flops I

Algebraic elliptic cohomology theory and flops I

We define the algebraic elliptic cohomology theory coming from Krichever’s elliptic genus as an oriented cohomology theory on smooth varieties over an arbitrary perfect field. We show that in the algebraic cobordism ring with rational coefficients, the ideal generated by differences of classical flo...

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Veröffentlicht in:Mathematische annalen 2019-12, Vol.375 (3-4), p.1823-1855
Hauptverfasser: Levine, Marc, Yang, Yaping, Zhao, Gufang, Riou, Joël
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Mathematics and Statistics
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container_title Mathematische annalen
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creator Levine, Marc
Yang, Yaping
Zhao, Gufang
Riou, Joël
description We define the algebraic elliptic cohomology theory coming from Krichever’s elliptic genus as an oriented cohomology theory on smooth varieties over an arbitrary perfect field. We show that in the algebraic cobordism ring with rational coefficients, the ideal generated by differences of classical flops coincides with the kernel of Krichever’s elliptic genus. This generalizes a theorem of B. Totaro in the complex analytic setting.
doi_str_mv 10.1007/s00208-019-01880-x
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subjects Algebra
Homology
Mathematics
Mathematics and Statistics
title Algebraic elliptic cohomology theory and flops I
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