134 research outputs found
Reductions of Shimura Varieties
The aim of this workshop was to discuss recent developments in the theory of reductions of Shimura varieties and related topics. The talks presented new methods and results that intertwine a multitude of topics such as geometry and cohomology of moduli spaces of abelian varieties, -divisible groups and Drinfeld shtukas, -adic Hodge theory, and the Langlands program
Towards a theory of local Shimura varieties
This is a survey article that advertizes the idea that there should exist a
theory of p-adic local analogues of Shimura varieties. Prime examples are the
towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also
review their theory in the light of this idea. We also discuss conjectures on
the -adic cohomology of local Shimura varieties.Comment: 53 page
On central leaves of Hodge-type Shimura varieties with parahoric level structure
Kisin and Pappas constructed integral models of Hodge-type Shimura varieties
with parahoric level structure at , such that the formal neighbourhood of
a mod~ point can be interpreted as a deformation space of -divisible
group with some Tate cycles (generalising Faltings' construction). In this
paper, we study the central leaf and the closed Newton stratum in the formal
neighbourhoods of mod~ points of Kisin-Pappas integral models with parahoric
level structure; namely, we obtain the dimension of central leaves and the
almost product structure of Newton strata. In the case of hyperspecial level
strucure (i.e., in the good reduction case), our main results were already
obtained by Hamacher, and the result of this paper holds for ramified groups as
well.Comment: 33 pages; section 2.5 added to fill in the gap in the earlier versio
The de Rham cohomology of the Suzuki curves
For a natural number , let be the th
Suzuki curve. We study the mod Dieudonn\'{e} module of ,
which gives the equivalent information as the Ekedahl-Oort type or the
structure of the -torsion group scheme of its Jacobian. We accomplish this
by studying the de Rham cohomology of . For all , we
determine the structure of the de Rham cohomology as a -modular
representation of the th Suzuki group and the structure of a submodule of
the mod Dieudonn\'{e} module. For and , we determine the complete
structure of the mod Dieudonn\'{e} module
Affine Grassmannians and the geometric Satake in mixed characteristic
We endow the set of lattices in Q_p^n with a reasonable algebro-geometric
structure. As a result, we prove the representability of affine Grassmannians
and establish the geometric Satake correspondence in mixed characteristic. We
also give an application of our theory to the study of Rapoport-Zink spaces.Comment: 63 pages. Fix a gap in the proof of Theorem A.29. A few more details
added and exposition improve
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