In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the p-adic pushforward of the Haar measure under a ...
Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d
Let A be a regular local ring containing 1/2, which is either equicharacteristic, or is smooth over a d.v.r. of mixed characteristic. We prove that the product maps on derived Grothendieck-Witt groups of A satisfy the following property: given two elements ...
In this work we study the oriented Chow groups. These groups were defined by J. Barge et F. Morel in order to understand when a projective module P of top rank over a ring A has a free factor of rank one, i.e is isomorphic to Q ⊕ A. We show first that thes ...