Roth's Theorem over arithmetic function fields

Abstract

Roth's theorem is extended to finitely generated field extensions of $\mathbb{Q}$, using Moriwaki's framework for heights.

84 pages; AmSTeX. v2: Lemma 7.6 replaced (now Lemmas 7.8 and 7.9); minor fixes and rearrangements; minor change in title. v3: Rewrote much of Proposition 8.9 (Now Lemmas 8.9-8.10 and Prop. 8.11) and parts of the Introduction; added Prop. 3.24 and Examples 4.12 and 4.13. v4: Addressed comments from a referee. Rewrote much of the second half of Section 3; fixed Lemma 6.5, Corollary 6.6, etc

References in corpus (3)

• Positive degree and arithmetic bigness
• Nagata's embedding theorem
• A geometric formulation of Siegel's diophantine theorem