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 fibre bundle with connection having meromorphic poles on D. Let p1,...,ps ∈ X(K) and X := X \ {D,p1,...,ps} (the pj’s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E–section of type α of the vector bundle E with respect to the points pj ; this is the natural generalization of the notion of E function defined in Siegel Shidlowski theory. We prove that the value of a E–section of type α in an algebraic point different from the pj’s has maximal transcendence degree. Siegel Shidlowski theorem is a special case of the theorem proved. We give an application to isomonodromic connections.

Gasbarri, C. (2013). Horizontal sections of connections on curves and transcendence. ACTA ARITHMETICA, 158(2), 99-128 [10.4064/aa158-2-1].

Horizontal sections of connections on curves and transcendence

GASBARRI, CARLO
2013-01-01

Abstract

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 fibre bundle with connection having meromorphic poles on D. Let p1,...,ps ∈ X(K) and X := X \ {D,p1,...,ps} (the pj’s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E–section of type α of the vector bundle E with respect to the points pj ; this is the natural generalization of the notion of E function defined in Siegel Shidlowski theory. We prove that the value of a E–section of type α in an algebraic point different from the pj’s has maximal transcendence degree. Siegel Shidlowski theorem is a special case of the theorem proved. We give an application to isomonodromic connections.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - Geometria
English
Gasbarri, C. (2013). Horizontal sections of connections on curves and transcendence. ACTA ARITHMETICA, 158(2), 99-128 [10.4064/aa158-2-1].
Gasbarri, C
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
sieg-shli03.pdf

non disponibili

Licenza: Copyright dell'editore
Dimensione 281.89 kB
Formato Adobe PDF
281.89 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/121059
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact