Journal article
Algebraic elliptic cohomology and flops II: SL-cobordism
M Levine, Y Yang, G Zhao
Advances in Mathematics | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2021
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.
Grants
Awarded by Horizon 2020 Framework Programme
Funding Acknowledgements
The authors Y.Y. and G.Z are grateful to Universitat Duisburg-Essen for hospitality and excellent working conditions, and for financial support via DFG Schwerpunktprogramm SPP 1786. We would like to thank Diarmuid Crowley for pointing out the reference [46], and for very useful discussions. Y.Y. was partially supported by the Australian Research Council (ARC) via the award DE190101231. G.Z. was partially supported by the ARC via the award DE190101222. M.L. was partially supported by the DFG through the grant LE 2259/7-2 and by the ERC through the project QUADAG. All three authors thank the referee for the detailed and very helpful comments, which have greatly improved this paper. This paper is part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 832833).