under construction
Let be the etale site of complex schemes of finite type. For a scheme, its infinitesimal site is the big site of the de Rham space :
the site whose objects are pairs of an affine and a morphism from its reduced part ( for the nilradical of ) into .
More generally, for positive characteristic, the definition is more involved than that.
The abelian sheaf cohomology over is the crystalline cohomology of .
An original account of the definition of the crystalline topos is section 7, page 299 of
A review of some aspects is in
and on page 7 of
In the article
it is shown that if is proper over an algebraically closed field of characteristic , and embeds into a smooth scheme over , then the infinitesimal cohomology of coincides with etale cohomology with coefficients in (or more generally if we work with the infinitesimal site of over ).
Last revised on March 30, 2011 at 08:47:59. See the history of this page for a list of all contributions to it.