Iitaka's $C_{n,m}$ conjecture for 3-folds over finite fields

Abstract

We prove Iitaka's $C_{n,m}$ conjecture for $3$-folds over the algebraic closure of finite fields. Along the way we prove some results on the birational geometry of log surfaces over nonclosed fields and apply these to existence of relative good minimal models of $3$-folds.

24 pages, references update

References in corpus (3)

• Behavior of canonical divisors under purely inseparable base changes
• Kodaira dimension of algebraic fiber spaces over abelian varieties
• Abundance theorem for surfaces over imperfect fields

Cited by in corpus (5)

• Abundance theorem for surfaces over imperfect fields
• Abundance for non-uniruled 3-folds with non-trivial Albanese maps in positive characteristics
• Minimal model program for excellent surfaces
• On the boundedness of anti-canonical volumes of singular Fano $3$-folds in characteristic $p>5$
• Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics