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Distributions on rational function fields

✍ Scribed by Steven Galovich; Michael Rosen


Publisher
Springer
Year
1981
Tongue
English
Weight
567 KB
Volume
256
Category
Article
ISSN
0025-5831

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Let M be a nonconstant polynomial in the polynomial ring R T =F q [T ] over the finite field F q . We show that the universal ordinary punctured distribution on 1 M R T Γ‚R T is a free abelian group and determine its rank. We also compute the torsion subgroups of the universal ordinary punctured even

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By means of GrΓΆbner basis techniques algorithms for solving various problems concerning subfields K (g) := K (g 1 , . . . , gm) of a rational function field K (x) := K (x 1 , . . . , xn) are derived: computing canonical generating sets, deciding field membership, computing the degree and separabilit

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A structure theorem on the Mordell-Weil group of abelian varieties which arise as the twists associated with various double covers of varieties is proved. As an application, a three-parameter family of elliptic curves whose generic Mordell-Weil rank is four is constructed. * 1995 Academic Press. Inc