On Grothendieck rings and algebraically constructible functions

Goulwen Fichou (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We investigate Grothendieck rings appearing in real geometry, notably for arc-symmetric sets, and focus on the relative case in analogy with the properties of the ring of algebraically constructible functions defined by McCrory and Parusinski. We study in particular the duality and link operators, including its behaviour with respect to motivic Milnor fibres with signs.

Mots clés: Grothendieck ring; constructible function; real algebraic geometry

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou. On Grothendieck rings and algebraically constructible functions. Mathematische Annalen, 2017, 369 (1-2), pp.761-795. ⟨10.1007/s00208-017-1564-9⟩. ⟨hal-01497606⟩