The Ordinary Limit for Varieties over Z[x_1,...,x_r]

Abstract

We investigate for families of smooth projective varieties over a localized polynomial ring Z[x_1,...,x_r][D^{-1}] the conjugate filtration on De Rham cohomology tensored with Z/NZ. As N tends to infinity this leads to the concept of the ordinary limit, which seems to be the non-archimedean analogue of the large complex structure limit