Erratum to: A note on Galois embeddings of abelian varieties
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DOI: 10.1007/s00229-018-1080-6
Abstract: The original Theorem in the article is revised in this erratum based on a referee’s request. read more here.
Keywords: embeddings abelian; note galois; abelian varieties; galois embeddings ... See more keywords
On a conjecture of Voisin on the gonality of very general abelian varieties
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DOI: 10.1016/j.aim.2020.107173
Abstract: We study orbits for rational equivalence of zero-cycles on very general abelian varieties by adapting a method of Voisin to powers of abelian varieties. We deduce that, for $k$ at least $3$, a very general… read more here.
Keywords: general abelian; voisin gonality; gonality general; abelian varieties ... See more keywords
Dynamical degrees of automorphisms on abelian varieties
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DOI: 10.1016/j.aim.2021.108082
Abstract: For any given Salem number, we construct an automorphism on a simple abelian variety whose first dynamical degree is the square of the Salem number. Our construction works for both simple abelian varieties with totally… read more here.
Keywords: simple abelian; abelian varieties; automorphisms abelian; dynamical degrees ... See more keywords
Fixed points and entropy of endomorphisms on simple abelian varieties
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DOI: 10.1016/j.jalgebra.2018.09.018
Abstract: In this paper we investigate fixed-point numbers and entropies of endomorphisms on abelian varieties. It was shown quite recently that the number of fixed-points of an iterated endomorphism on a simple complex torus is either… read more here.
Keywords: number; points entropy; fixed points; simple abelian ... See more keywords
Computational algorithm for reduction type of CM abelian varieties
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DOI: 10.1016/j.jalgebra.2019.08.032
Abstract: Abstract Let A be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number p. Denote A as an abelian variety over a finite field of… read more here.
Keywords: reduction; reduction type; computational algorithm; abelian varieties ... See more keywords
The characteristic polynomials of abelian varieties of higher dimension over finite fields
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DOI: 10.1016/j.jnt.2018.09.014
Abstract: Abstract The characteristic polynomials of abelian varieties over the finite field F q with q = p n elements have a lot of arithmetic and geometric information. They have been explicitly described for abelian varieties… read more here.
Keywords: dimension; polynomials abelian; varieties higher; characteristic polynomials ... See more keywords
Torsion for abelian varieties of type III
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DOI: 10.1016/j.jnt.2018.10.017
Abstract: Abstract Let A be an abelian variety defined over a number field K. The number of torsion points that are rational over a finite extension L is bounded polynomially in terms of the degree [… read more here.
Keywords: varieties type; mumford tate; type iii; abelian varieties ... See more keywords
Product formulas for periods of CM abelian varieties and the function field analog
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DOI: 10.1016/j.jnt.2020.06.017
Abstract: Abstract We survey Colmez's theory and conjecture about the Faltings height and a product formula for the periods of abelian varieties with complex multiplication, along with the function field analog developed by the authors. In… read more here.
Keywords: periods abelian; abelian varieties; field analog; product ... See more keywords
Variétés abéliennes CM et grosse monodromie finie sauvage
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DOI: 10.1016/j.jnt.2022.01.007
Abstract: In this paper we study the wild part of the finite monodromy groups of abelian varieties over number fields. We solve Grunwald problems for groups of the form $\mathbf{Z}/p\mathbf{Z}\wr \mathfrak{S}_n$ over number fields to build… read more here.
Keywords: grosse monodromie; vari liennes; liennes grosse; finite monodromy ... See more keywords
SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES
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DOI: 10.1017/fms.2018.13
Abstract: In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this… read more here.
Keywords: metric families; abelian varieties; biextension metric; singularities biextension ... See more keywords
Angehrn-Siu-Helmke’s method applied to abelian varieties
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DOI: 10.1017/fms.2023.34
Abstract: Abstract We apply Angehrn-Siu-Helmke’s method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. We showed that a conjecture of Caucci holds for very general polarized abelian varieties in the moduli spaces $\mathcal… read more here.
Keywords: siu helmke; abelian varieties; helmke method; angehrn siu ... See more keywords