Horizontal sections of connections on curves and transcendence

• Autorzy: C. Gasbarri
• Języki publikacji: EN

Abstrakty

EN

Let K be a number field, X be a smooth projective curve over it and D be a reduced divisor on X. Let (E,∇) be a vector bundle with connection having meromorphic singularities on D. Let $p_1,...,p_s ∈ X(K)$ and $X^o:=X̅∖{D,p_1,..., p_s}$ (the $p_j$'s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E-section of arithmetic type of the vector bundle E with respect to the points $p_j$; this is the natural generalization of the notion of E-function defined in Siegel-Shidlovskiĭ theory. We prove that the value of an E-section of arithmetic type at an algebraic point different from the $p_j$'s has maximal transcendence degree. The Siegel-Shidlovskiĭ theorem is a special case of our theorem proved. We give two applications of the theorem.

Kategorie tematyczne

• 11J91: Transcendence theory of other special functions
• 30D35: Distribution of values, Nevanlinna theory
• 14G40: Arithmetic varieties and schemes; Arakelov theory; heights

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 2
• Strony: 99-128

Daty

wydano

2013

Twórcy

autor

C. Gasbarri

• Université de Strasbourg, IRMA, 7 rue René Descartes, 67084 Strasbourg, France

Identyfikatory

DOI

10.4064/aa158-2-1