Stably rational algebraic tori

— We relate R-equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.. R ´

The dynamics of a linear foliation is well understood; in particular, either every leaf is dense in the ambient torus, or every leaf is dense in a real codimension one subtorus,

Free homotopy classes of rational functions N We compute here the set P1 , P1 of naive homotopy classes of free i.e., unpointed endomorphisms of P1.. The result is mostly a

To prove that "^\ is dense in Y^, we consider some (/,/?)e^, and a non trivial invariant subset J of 13 Ul4, such that /iy(Wj(/)) is equal to a non trivial A-invariant

reported a new descent mode, that appears for holed disks of low moment of inertia around a diameter, where the ring fall vertically with periodic ve- locity uctuations as

Combining theorem 1.1 with the estimate on the sum of the degrees of the maximal torsion varieties of V ([Amo-Via 2009], corollary 5.3), we can give the following complete

In this section, as a supplement to the main theorems stated in Sec- tion 1, we give a yet another result of the failure of stable rationality of smooth weighted hypersurfaces,

Moreover if the representation is equidimensional, then so is the action (V/[G, G], G/[G, G]). Thus, in order to study Popov conjecture for non-semisimple groups, it is natural to