Integral Points of Projective Spaces Omitting Hyperplanes over Function Fields of Positive Characteristic

✍ Scribed by Julie Tzu-Yueh Wang

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 144 KB
• Volume: 77
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1999.2400

✦ Synopsis

We apply the S-unit theorem for a function field K with positive characteristic to show that under certain conditions the height of the S-integral points of P n (K)&[2n+2 hyperplanes in general position] is bounded. We also provide examples to show that the conditions are necessary.

1999 Academic Press

Let S be a finite set of points of C. An element f # K is said to be an S-unit if v P ( f )=0 for all P Â S.

We now recall the definition of (S, D)-integral points. (cf. [Voj]).