Rational points on varieties
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چکیده
منابع مشابه
On the number of rational points on Prym varieties over finite fields
We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.
متن کاملThe Minimum and Maximum Number of Rational Points on Jacobian Surfaces over Finite Fields
We give some bounds on the numbers of rational points on abelian varieties and jacobians varieties over finite fields. The main result is that we determine the maximum and minimum number of rational points on jacobians varieties of dimension 2.
متن کاملMirror Congruence For Rational Points On Calabi-Yau Varieties
One of the basic problems in arithmetic mirror symmetry is to compare the number of rational points on a mirror pair of Calabi-Yau varieties. At present, no general algebraic geometric definition is known for a mirror pair. But an important class of mirror pairs comes from certain quotient construction. In this paper, we study the congruence relation for the number of rational points on a quoti...
متن کاملGroups of Rational Points on Abelian Varieties over Finite Fields
Fix an isogeny class of abelian varieties with commutative endomorphism algebra over a finite field. This isogeny class is determined by a Weil polynomial fA without multiple roots. We give a classification of groups of rational points on varieties from this class in terms of Newton polygons of fA(1− t).
متن کاملOn the Number of Rational Points on Drinfeld Modular Varieties over Finite Fields
Drinfeld and Vladut proved that Drinfeld modular curves have many Fq2 -rational points compared to their genera. We propose a conjectural generalization of this result to higher dimensional Drinfeld modular varieties, and prove a theorem giving some evidence for the conjecture.
متن کاملVersality of Algebraic Group Actions and Rational Points on Twisted Varieties
We formalize and study several competing notions of versality for an action of a linear algebraic group on an algebraic variety X. Our main result is that these notions of versality are equivalent to various statements concerning rational points on twisted forms of X (existence of rational points, existence of a dense set of rational points, etc.) We give applications of this equivalence in bot...
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تاریخ انتشار 2008