16 research outputs found
Discrete invariants of varieties in positive characteristic
If is a scheme of characteristic , we define an -zip over to be
a vector bundle with two filtrations plus a collection of semi-linear
isomorphisms between the graded pieces of the filtrations. For every smooth
proper morphism satisfying certain conditions the de Rham bundles
have a natural structure of an -zip. We give a
complete classification of -zips over an algebraically closed field by
studying a semi-linear variant of a variety that appears in recent work of
Lusztig. For every -zip over our methods give a scheme-theoretic
stratification of . If the -zip is associated to an abelian scheme over
the underlying topological stratification is the Ekedahl-Oort
stratification. We conclude the paper with a discussion of several examples
such as good reductions of Shimura varieties of PEL type and K3-surfaces.Comment: 35 pages, minor changes in exposition, major changes to introductio
Classification of Reductive Monoid Spaces Over an Arbitrary Field
In this semi-expository paper we review the notion of a spherical space. In
particular we present some recent results of Wedhorn on the classification of
spherical spaces over arbitrary fields. As an application, we introduce and
classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio