RIGID ANALYTIC PICARD THEOREMS By WILLIAM CHERRY and MIN RU

نویسنده

  • Steven Lu
چکیده

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 that there are no nonconstant rigid analytic maps from the affine line to Abelian varieties. Furthermore, we use the lemma to prove new theorems of little and big Picard type for dominant mappings, in close analogy with Griffiths and King. For the little Picard type theorem, we prove that if X is a smooth projective variety with a simple normal crossings divisor D such that (X, D) has nonnegative logarithmic Kodaira dimension, then there are no dominant rigid analytic maps f from Am to X \ D. For the big Picard type theorem, we prove that if Y is a nonsingular rigid analytic space, E is an effective simple normal crossings divisor on Y , and if X is a smooth projective variety with a simple normal crossings divisor D such that (X, D) is of log-general type, then any dominant rigid analytic map f : Y \ E → X \ D extends to an analytic map from Y to X.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

Non-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 کامل

Lectures on Holomorphic Curves in Abelian Varieties National Central University Jhongli, Taiwan

* It is my pleasure to acknowledge the generous financial support provided by Academia Sinica and National Central University which made these lectures possible. These lectures are largely based on Min Ru's concise exposition of the subject in [Ru].

متن کامل

Non-Archimedean analytic curves in Abelian varieties

One of the main subtleties of non-Archimedean analysis is that the natural topology that one puts on non-Archimedean analytic spaces is totally disconnected, meaning that there is a base for the topology consisting of sets which are both open and closed. This makes it difficult, for instance, to define a good notion of analytic function so that one has analytic continuation properties. Of cours...

متن کامل

Vector Bundles over Analytic Character Varieties

Let Qp ⊆ L ⊆ K ⊆ Cp be a chain of complete intermediate fields where Qp ⊆ L is finite and K discretely valued. Let Z be a one dimensional finitely generated abelian locally L-analytic group and let ẐK be its rigid Kanalytic character group. Generalizing work of Lazard we compute the Picard group and the Grothendieck group of ẐK . If Z = o, the integers in L 6= Qp, we find Pic(ôK) = Zp which ans...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997