Corpus ID: 119600208

# Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties

@article{Li2018NewtonPS,
title={Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties},
author={Wanlin Li and Elena Mantovan and Rachel J. Pries and Yunqing Tang},
journal={arXiv: Number Theory},
year={2018}
}
We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo $p$ reduction of certain PEL-type Shimura varieties. We develop a clutching method to show that the intersection of the Torelli locus with some Newton polygon strata is non-empty and has the expected codimension. This yields results about the Newton polygon stratification of Hurwitz spaces of cyclic covers of the projective line. The clutching method allows us to guarantee the existence of a… Expand
5 Citations
Newton polygons arising from special families of cyclic covers of the projective line
• Mathematics
• Research in Number Theory
• 2019
By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Shimura variety. ForExpand
Some unlikely intersections between the Torelli locus and Newton strata in 𝒜 g
Let p be an odd prime. What are the possible Newton polygons for a curve in characteristic p? Equivalently, which Newton strata intersect the Torelli locus in Ag? In this note, we study the NewtonExpand
Some unlikely intersections between the Torelli locus and Newton strata in $\mathcal{A}_g$
Let $p$ be an odd prime. What are the possible Newton polygons for a curve in characteristic $p$? Equivalently, which Newton strata intersect the Torelli locus in $\mathcal{A}_g$? In this note, weExpand
Every $BT_1$ group scheme appears in a Jacobian
• Mathematics
• 2021
Let $p$ be a prime number and let $k$ be an algebraically closed field of characteristic $p$. A $BT_1$ group scheme over $k$ is a finite commutative group scheme which arises as the kernel of $p$ onExpand
On $BT_1$ group schemes and Fermat Jacobians
• Mathematics
• 2020
Let $p$ be a prime number and let $k$ be an algebraically closed field of characteristic $p$. A $BT_1$ group scheme over $k$ is a finite commutative group scheme which arises as the kernel of $p$ onExpand

#### References

SHOWING 1-10 OF 44 REFERENCES
Newton polygons arising from special families of cyclic covers of the projective line
• Mathematics
• Research in Number Theory
• 2019
By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Shimura variety. ForExpand
On the cohomology of certain PEL-type Shimura varieties
In this article we study the local geometry at a prime p of PEL-type Shimura varieties for which there is a hyperspecial level subgroup. We consider the Newton polygon stratification of the specialExpand
Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points
• Mathematics
• Association for Women in Mathematics Series
• 2019
We review the Shimura–Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched atExpand
Current results on Newton polygons of curves
There are open questions about which Newton polygons and Ekedahl-Oort types occur for Jacobians of smooth curves of genus $g$ in positive characteristic $p$. In this chapter, I survey the currentExpand
Ekedahl–Oort and Newton strata for Shimura varieties of PEL type
• Mathematics
• 2010
We study the Ekedahl–Oort stratification for good reductions of Shimura varieties of PEL type. These generalize the Ekedahl–Oort strata defined and studied by Oort for the moduli space of principallyExpand
The almost product structure of Newton strata in the Deformation space of a Barsotti–Tate group with crystalline Tate tensors
In this paper, we construct the almost product structure of the minimal Newton stratum in deformation spaces of Barsotti–Tate groups with crystalline Tate tensors, similar to Oort’s and Mantovan’sExpand
Arithmetic Compactifications of PEL-Type Shimura Varieties
By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logicalExpand
Ordinariness in good reductions of Shimura varieties of PEL-type
Abstract The main purpose of this paper is the definition of the μ-ordinary locus in good reductions of Shimura varieties of PEL-type and the proof that this locus is open and dense. This generalizesExpand
Points on some Shimura varieties over finite fields
The Hasse-Weil zeta functions of varieties over number fields are conjecturally products (and quotients) of automorphic L-functions. For a Shimura variety S associated to a connected reductive groupExpand
Cycles on Shimura varieties via geometric Satake
• Mathematics
• 2017
We construct (cohomological) correspondences between mod $p$ fibers of different Shimura varieties and describe the fibers of these correspondences by studying irreducible components of affineExpand