Abstract:

We will show that for a finite field extension L of a perfect field k, the Weil restriction
from L to k of certain cellular smooth L-schemes admit a canonical cellular structure. Just
the case of the Weil restriction of the projective line is already very interesting. This leads
to some interesting new computations of some cellular homology sheaves ; we will explain the
case of L being a quadratic extension and deduce that K^{MW}_1 \otimes \Z[L] is isomorphic to
(K^{MW}_1) ^[L] . This computation also prove a conjecture of myself and Anand Sawant on orientable
smooth projective A^1 connected k-schemes in dimension 2.

This is work in progress with Anand Sawant.