Journal article

Algebraic elliptic cohomology theory and flops I

Marc Levine, Yaping Yang, Gufang Zhao, Joel Riou

MATHEMATISCHE ANNALEN | SPRINGER HEIDELBERG | Published : 2019

Abstract

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.

Grants

Funding Acknowledgements

The authors Yang and Zhao are grateful to Universitat Duisburg-Essen for hospitality and excellent working conditions. The author Levine thanks the Humboldt Foundation for its support.