Big Picard theorem for jet differentials and non-archimedean Ax-Lindemann theorem

被引：0

作者：

Huynh, Dinh Tuan ^{[1
]}

Sun, Ruiran ^{[2
]}

Xie, Song-Yan ^{[3
,4
,5
]}

机构：

[1] Hue Univ, Univ Educ, Dept Math, 34 Le Loi St, Hue City, Vietnam

[2] McGill Univ, Dept Math & Stat, Montreal, PQ, Canada

[3] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[4] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China

[5] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2023年 / 253卷

关键词：

Nevanlinna theory; Jet differentials; Non-archimedean; Picard theorem; Hyperbolicity; Ax-Lindemann theorem; Abelian varieties; SEMI-ABELIAN VARIETIES; ANDRE-OORT CONJECTURE; CURVES; FLOWS;

D O I：

10.1016/j.jnt.2023.06.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By implementing jet differential techniques in non-archimede-an geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As applications, we establish two hyperbolicity-related results. Firstly, we prove a non-archimedean Ax-Lindemann theorem for totally degenerate abelian varieties. Secondly, we show the pseudo-Borel hyperbolicity for subvarieties of general type in abelian varieties.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页码：257 / 277

页数：21

共 41 条

[1] Algebraic degeneracy of non-Archimedean analytic maps [J].

An, Ta Thi Hoai ;

Cherry, William ;

Wang, Julie Tzu-Yueh .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2008, 19 (03) :481-492

[2] SCHANUELS CONJECTURES [J].

AX, J .

ANNALS OF MATHEMATICS, 1971, 93 (02) :252-&

[3]

BLOCH A, 1926, J MATH, V5, P19

[4]

Borel Armand., 1972, Journal of Di erential Geometry, V6, P543, DOI [10.4310/jdg/1214430642, DOI 10.4310/JDG/1214430642]

[5] DEGENERATING ABELIAN-VARIETIES [J].

BOSCH, S ;

LUTKEBOHMERT, W .

TOPOLOGY, 1991, 30 (04) :653-698

[6] A nonarchimedean Ax-Lindemann theorem [J].

Chambert-Loir, Antoine ;

Loeser, Francois .

ALGEBRA & NUMBER THEORY, 2017, 11 (09) :1967-1999

[7] NON-ARCHIMEDEAN ANALYTIC CURVES IN ABELIAN-VARIETIES [J].

CHERRY, W .

MATHEMATISCHE ANNALEN, 1994, 300 (03) :393-404

[8] Rigid analytic Picard theorems [J].

Cherry, W ;

Ru, M .

AMERICAN JOURNAL OF MATHEMATICS, 2004, 126 (04) :873-889

[9]

CHERRY W, 2002, CONT MATH, V303, P7

[10] A multivariate Faa di Bruno formula with applications [J].

Constantine, GM ;

Savits, TH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (02) :503-520

← 1 2 3 4 5 →