Variations on a question of Larsen and Lunts

Julien Sebag (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Let k be a field of characteristic zero. Let X and X' be two k-schemes of finite type having the same class in the Grothendieck ring of varieties. Is it true that X and X' are piecewise isomorphic? This question, originally asked by Larsen and Lunts, and some of its consequences constitute the subject of this article.

Domaines: Géométrie algébrique [math.AG]

Julien Sebag. Variations on a question of Larsen and Lunts. Proceedings of the American Mathematical Society, 2010, 138 (4), pp.1231-1242. ⟨10.1090/S0002-9939-09-10179-X⟩. ⟨hal-01414543⟩