The paper proves new results on the irreducibility of fibers of a cover of an algebraic group, above a cyclic subgroup. This provides entirely new versions of Hilbert Irreducibility, settling in particular a conjecture of Pisot. Also, a Bertini Theorem for covers of multiplicative tori is deduced. The methods are completely different from previously used ones.

Hilbert irreducibility above algebraic groups.

ZANNIER, UMBERTO
2010

Abstract

The paper proves new results on the irreducibility of fibers of a cover of an algebraic group, above a cyclic subgroup. This provides entirely new versions of Hilbert Irreducibility, settling in particular a conjecture of Pisot. Also, a Bertini Theorem for covers of multiplicative tori is deduced. The methods are completely different from previously used ones.
2010
Diophantine geometry; Irreducibility; Algebraic groups
File in questo prodotto:
File Dimensione Formato  
Duke.2010.HIT.DMJ153i2.pdf

Accesso chiuso

Tipologia: Altro materiale allegato
Licenza: Non pubblico
Dimensione 249.12 kB
Formato Adobe PDF
249.12 kB Adobe PDF   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/11384/64
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 25
  • ???jsp.display-item.citation.isi??? 22
  • OpenAlex ND
social impact