  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.
