Algebraic elliptic cohomology and flops II: SL-cobordism

Abstract

In this paper, we study the algebraic Thom spectrum MSL in Voevodsky's motivic stable homotopy category over an arbitrary perfect field k. Using the motivic Adams spectral sequence, we compute the geometric part of the η-completion of MSL. As an application, we study Krichever's elliptic genus with integral coefficients, restricted to MSL. We determine its image, and identify its kernel as the ideal generated by differences of SL-flops. This was proved by B. Totaro in the complex analytic setting. In the appendix, we prove some convergence properties of the motivic Adams spectral sequence.