共查询到20条相似文献,搜索用时 15 毫秒
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José Felipe Voloch 《Bulletin of the Brazilian Mathematical Society》1998,29(2):295-300
For ordinary abelian varieties in characteristicp>0, we define an analogue of the period lattice and of the parametrization by
g
and give some applications. 相似文献
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Sergey Rybakov 《Central European Journal of Mathematics》2010,8(2):282-288
Let A be an abelian variety with commutative endomorphism algebra over a finite field k. The k-isogeny class of A is uniquely determined by a Weil polynomial f A without multiple roots. We give a classification of the groups of k-rational points on varieties from this class in terms of Newton polygons of f A (1 − t). 相似文献
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Safia Haloui 《Journal of Number Theory》2010,130(12):2745-2752
We describe the set of characteristic polynomials of abelian varieties of dimension 3 over finite fields. 相似文献
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Davide Lombardo 《The Ramanujan Journal》2017,43(2):383-403
We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic extensions of a number field K and extensions of K generated by torsion points of an abelian variety over K. We prove that the property called \((\mu )\) in Hindry and Ratazzi (J Ramanujan Math Soc 25(1):81–111, 2010) holds for any abelian variety, while the same is not true for the stronger version of the property introduced in Hindry and Ratazzi (J Inst Math Jussieu 11(1):27–65, 2012). 相似文献
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An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group. An early version of this article was inadvertently published before all the revisions had been completed and then retracted [https://doi.org/10.1007/s00013-018-1244-3]. This article is the final peer reviewed version.
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Yu. G. Zarkhin 《Mathematical Notes》1976,19(3):240-244
In this paper Tate's finiteness conjecture for isogenies of polarized Abelian varieties in characteristic p>2 is proved. From this conjecture it is deduced that Tate modules are semisimple and that Tate's conjecture on the homomorphisms of Abelian varieties is valid.Translated from Matematicheskie Zametki, Vol. 19, No. 3, pp. 393–400, March, 1976. 相似文献
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Yu. G. Zarkhin 《Mathematical Notes》1977,22(1):493-498
The finiteness of the torsion of Abelian varieties with a complete real field of endomorphisms in the maximal Abelian extension of the field of definition is proven. This assertion is formally deduced from the finiteness hypothesis for isogenic Abelian varieties, proven for characteristic p > 2. The structure is studied of the Lie algebra of Galois groups acting in a Tate module; in particular, for fields of characteristic greater than two there is proven one-dimensionality of the center of the Lie algebra.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 3–11, July, 1977. 相似文献
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M. Gromov 《Journal of the European Mathematical Society》1999,1(2):109-197
The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory, algebraic geometry, and symbolic dynamics. Received August 3, 1998 / final version received January 22, 1999 相似文献