Unifying the little Picard, Lohwater–Pommerenke and Brody theorems
نویسندگان
چکیده
منابع مشابه
Rigid Analytic Picard Theorems
We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem [Ber, Theorem 4.5.1], which says there are no nonconstant rigid analytic maps from the affine line to non-singular projective curves of positive genus, ...
متن کاملNon-archimedean Big Picard Theorems
A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich’s theory of non-Archimedean analytic spaces.
متن کاملFiniteness theorems for the Picard objects of an algebraic stack
We prove some finiteness theorems for the Picard functor of an algebraic stack, in the spirit of SGA6, exp. XII and XIII. In particular, we give a stacky version of Raynaud’s relative representability theorem, we give sufficient conditions for the existence of the torsion component of the Picard functor, and for the finite generation of the Néron-Severi groups or of the Picard group itself. We ...
متن کاملRIGID ANALYTIC PICARD THEOREMS By WILLIAM CHERRY and MIN RU
We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem, which says there are no nonconstant rigid analytic maps from the affine line to nonsingular projective curves of positive genus, and of Cherry’s result...
متن کاملA Unifying View of Representer Theorems
It is known that the solution of regularization and interpolation problems with Hilbertian penalties can be expressed as a linear combination of the data. This very useful property, called the representer theorem, has been widely studied and applied to machine learning problems. Analogous optimality conditions have appeared in other contexts, notably in matrix regularization. In this paper we p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.05.045