Bertini theorems over finite fields
نویسندگان
چکیده
منابع مشابه
Bertini Theorems over Finite Fields
Let X be a smooth quasiprojective subscheme of P of dimension m ≥ 0 over Fq. Then there exist homogeneous polynomials f over Fq 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 ζX(m + 1) −1, where ζX(s) = ZX(q −s) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming ...
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Let k be an infinite field of arbitrary characteristic, (A,M, K) a k-algebra of essentially finite type, with K/k separable and P a local property. We say that LBk(P) holds if: For the generic α = (α1, . . . , αn) ∈ k ⇒ P(AxαA) ⊆ P(A)∩V (xα)∩ UP (xα = ∑ αixi, 〈x1, . . . , xn〉 = M, UP non-empty open subset of SpecA and P(A) = {P ∈ SpecA|Ap is P}). We show that: LBK(P) holds ⇒ LBK(GP) holds for t...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2004
ISSN: 0003-486X
DOI: 10.4007/annals.2004.160.1099