Motivic invariants of birational maps


We construct invariants of birational maps with values in the Kontsevich–Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are well-suited to investigating the structure of the Grothendieck ring and L-equivalence. Building on known constructions of L-equivalence, we prove new unexpected results about Cremona groups.


Hsueh-Yung Lin

Department of Mathematics, National Taiwan University and National Center for Theoretical Sciences, Taipei, Taiwan

Evgeny Shinder

School of Mathematics and Statistics, University of Sheffield, Sheffield, UK and Hausdorff Center for Mathematics at the University of Bonn, Bonn, Germany