Purity of level m stratifications

Details Purity of level m stratifications Purity of level m stratifications

2008-08-12

arxiv.org/abs/0808.1629v2

Mathematics

Algebraic Geometry

Final version 38 pages. To appear in Ann. Sci. \'Ec. Norm. Sup

Scientific paper

Let $k$ be a field of characteristic $p>0$. Let $D_m$ be a $\BT_m$ over $k$ (i.e., an $m$-truncated Barsotti--Tate group over $k$). Let $S$ be a\break $k$-scheme and let $X$ be a $\BT_m$ over $S$. Let $S_{D_m}(X)$ be the subscheme of $S$ which describes the locus where $X$ is locally for the fppf topology isomorphic to $D_m$. If $p\ge 5$, we show that $S_{D_m}(X)$ is pure in $S$ i.e., the immersion $S_{D_m}(X) \hookrightarrow S$ is affine. For $p\in\{2,3\}$, we prove purity if $D_m$ satisfies a certain property depending only on its $p$-torsion $D_m[p]$. For $p\ge 5$, we apply the developed techniques to show that all level $m$ stratifications associated to Shimura varieties of Hodge type are pure.

Affiliated with

Also associated with

No associations

Rating

Purity of level m stratifications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Purity of level m stratifications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Purity of level m stratifications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-202739