منابع مشابه
Smooth Ideals in Hyperelliptic Function Fields Smooth Ideals in Hyperelliptic Function Fields
Recently, several algorithms have been suggested for solving the discrete logarithm problem in the Jacobians of high-genus hyperelliptic curves over nite elds. Some of them have a provable subexponential running time and are using the fact that smooth reduced ideals are suuciently dense. We explicitly show how these density results can be derived. All proofs are purely combinatorial and do not ...
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Recently, several algorithms have been suggested for solving the discrete logarithm problem in the Jacobians of high-genus hyperelliptic curves over finite fields. Some of them have a provable subexponential running time and are using the fact that smooth reduced ideals are sufficiently dense. We explicitly show how these density results can be derived. All proofs are purely combinatorial and d...
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Given a countable Borel equivalence relation E on a Polish space, let IE denote the σ-ideal generated by the Borel partial transversals of E. We show that there is a Borel homomorphism from IE to IF if and only if there is a smooth-to-one Borel homomorphism from a finite index Borel subequivalence relation of E to F . As a corollary, we see that IE is homogeneous in the sense of Zapletal (2007,...
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Let f = (f 1 ; : : : ; f m) be a holomorphic mapping in a neighborhood of the origin in C n. We nd suucient condition, in terms of residue currents, for a smooth function to belong to the ideal in C k generated by f. If f is a complete intersection the condition is essentially necessary. More generally we give suucient condition for an element of class C k in the Koszul complex induced by f to ...
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Let R be an n-dimensional regular local domain essentially of finite type over a ground field k of characteristic zero, and let ν be a rank one valuation centered on R. Recall that this is equivalent to asking that ν be an R-valued valuation on the fraction field K of R, taking non-negative values on R and positive values on the maximal ideal m ⊆ R. A theorem of Zariski and Abhyankar states tha...
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ژورنال
عنوان ژورنال: Journal of Korean Institute of Intelligent Systems
سال: 2002
ISSN: 1976-9172
DOI: 10.5391/jkiis.2002.12.1.090