Given a sequence of algebraic points f(n) of a variety X over a characteristic 0-function field K of unbounded (normalised) height, we construct a limiting derivative in P(Omega(1)(X/K)). The real (Oesterle, 2002 [4]) "a, b, c" conjecture over function fields is an immediate corollary. In principle, every Mordellic problem over function fields reduces to a hyperbolicity problem on the generic fibre by way of the said construction, but, unfortunately, such a conclusion is delicate in the presence of bad reduction. This - as found in McQuillan (2001) [3, 4.3] - together with an alternative approach to the "a, b, c" conjecture by K. Yamanoi (2004) [5] has already been reported in the Seminaire Bourbaki (Gasbarri, 2008 [1])

Mcquillan, M. (2013). Differentiating relatively. COMPTES RENDUS MATHÉMATIQUE, 351(13-14), 523-526 [10.1016/j.crma.2013.05.003].

Differentiating relatively

MCQUILLAN, MICHAEL
2013

Abstract

Given a sequence of algebraic points f(n) of a variety X over a characteristic 0-function field K of unbounded (normalised) height, we construct a limiting derivative in P(Omega(1)(X/K)). The real (Oesterle, 2002 [4]) "a, b, c" conjecture over function fields is an immediate corollary. In principle, every Mordellic problem over function fields reduces to a hyperbolicity problem on the generic fibre by way of the said construction, but, unfortunately, such a conclusion is delicate in the presence of bad reduction. This - as found in McQuillan (2001) [3, 4.3] - together with an alternative approach to the "a, b, c" conjecture by K. Yamanoi (2004) [5] has already been reported in the Seminaire Bourbaki (Gasbarri, 2008 [1])
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - Geometria
fre
L'articolo era l'oggetto del seminario Bourbaki No. 326  (2009), Exp. No. 989, viii
Mcquillan, M. (2013). Differentiating relatively. COMPTES RENDUS MATHÉMATIQUE, 351(13-14), 523-526 [10.1016/j.crma.2013.05.003].
Mcquillan, M
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
my2cras.pdf

non disponibili

Descrizione: Articolo principale
Licenza: Copyright dell'editore
Dimensione 193.22 kB
Formato Adobe PDF
193.22 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: http://hdl.handle.net/2108/90242
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact