Tensor Decomposition of Isocrystals Characterizes Mumford Curves
نویسنده
چکیده
We seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics via characterizing curves in positive characteristics which are reduction of Shimura curve over C. In this paper, we study the liftablity of a curve in the moduli space of principally polarized abelian varieties over k, char k = p. We show that in the generic ordinary case, some tensor decomposition of the isocrystal associated to the family imply that this curve can be lifted to a Shimura curve.
منابع مشابه
A Characterization of Mumford Curves with Good Reduction
Mumford defines a certain type of Shimura curves of Hodge type, parametrizing polarized complex abelian fourfolds. It is the first example of non-PEL type Shimura varieties. In this paper, we study the good reduction of such curve in positive characteristics and give a characterization: a family has maiximal Higgs field and the corresponding Dieudonne crystal admits a special tensor decompositi...
متن کاملOverholonomicity of overconvergent F-isocrystals over smooth varieties
We prove the overholonomicity of overconvergent F-isocrystals over smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent F-isocrystals are equivalent. Then the overholonomicity is stable under tensor products. So, the overholonomicity gives a p-adic cohomology stable under Grothendieck’s cohomological operations.
متن کاملA simple form of MT impedance tensor analysis to simplify its decomposition to remove the effects of near surface small-scale 3-D conductivity structures
Magnetotelluric (MT) is a natural electromagnetic (EM) technique which is used for geothermal, petroleum, geotechnical, groundwater and mineral exploration. MT is also routinely used for mapping of deep subsurface structures. In this method, the measured regional complex impedance tensor (Z) is substantially distorted by any topographical feature or small-scale near-surface, three-dimensional (...
متن کاملThe Hodge Conjecture for General Prym Varieties
We work over C, the field of complex numbers. The Prym variety of a double cover C → D of a smooth connected projective curve D by a smooth connected curve C is defined (see [7]) as the identity component of the kernel of the norm homomorphism N : J(C) → J(D) between the Jacobians of the curves. This is an abelian variety polarised by the restriction of the canonical polarisation on J(C); we de...
متن کاملAlgorithms for Mumford curves
Mumford showed that Schottky subgroups of PGL(2,K) give rise to certain curves, now called Mumford curves, over a non-archimedean field K. Such curves are foundational to subjects dealing with nonarchimedean varieties, including Berkovich theory and tropical geometry. We develop and implement numerical algorithms for Mumford curves over the field of p-adic numbers. A crucial and difficult step ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013