Algebraic elliptic cohomology theory and flops, I

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.