Bertini theorems over finite fields

• 成果类型: Article
• 署名作者: Poonen, B
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.160.1099
• 发表日期: 2004
• 页码: 1099-1127
• 关键词: space-filling curves; VARIETIES

摘要

Let X be a smooth quasiprojective subscheme of P-n of dimension M >= 0 over F-q. Then there exist homogeneous polynomials f over F-q for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to zeta x (m+ 1)(-1), where zeta(X) (s) = Z(X) (q(-s)) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming the abc conjecture and another conjecture.