64,465 research outputs found
Perfectoid Shimura varieties of abelian type
We prove that Shimura varieties of abelian type with infinite level at
are perfectoid. As a corollary, the moduli spaces of polarized K3 surfaces with
infinite level at are also perfectoid.Comment: 37 pages; slightly revised version, to appear in IMR
Cell decomposition of some unitary group Rapoport-Zink spaces
In this paper we study the -adic analytic geometry of the basic unitary
group Rapoport-Zink spaces \M_K with signature . Using the theory of
Harder-Narasimhan filtration of finite flat groups developed by Fargues in
\cite{F2},\cite{F3}, and the Bruhat-Tits stratification of the reduced special
fiber \M_{red} defined by Vollaard-Wedhorn in \cite{VW}, we find some
relatively compact fundamental domain \D_K in \M_K for the action of
G(\Q_p)\times J_b(\Q_p), the product of the associated -adic reductive
groups, and prove that \M_K admits a locally finite cell decomposition. By
considering the action of regular elliptic elements on these cells, we
establish a Lefschetz trace formula for these spaces by applying Mieda's main
theorem in \cite{Mi2}.Comment: some minor errors are corrected; to appear in Math. An
-adic families of automorphic forms over some unitary Shimura varieties
We construct some -dimensional eigenvarieties for finite slope
overconvergent eigenforms over some unitary Shimura varieties with signature
by adapting
Andreatta-Iovita-Pilloni's method. We also show that there are some Galois
pseudo-characters over our eigenvarieties by studying analytic continuation of
finite slope eigenforms over these Shimura varieties.Comment: 24 pages; revised version; minor changes; to appear in Math. Research
Letter
Weak universality of dynamical : non-Gaussian noise
We consider a class of continuous phase coexistence models in three spatial
dimensions. The fluctuations are driven by symmetric stationary random fields
with sufficient integrability and mixing conditions, but not necessarily
Gaussian. We show that, in the weakly nonlinear regime, if the external
potential is a symmetric polynomial and a certain average of it exhibits
pitchfork bifurcation, then these models all rescale to near their
critical point.Comment: 37 pages; updated introduction and reference
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