Results 1 to 10 of about 443 (25)
The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type
Forum of Mathematics, Sigma, 2021 In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$-type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov ...
Rafael von Känel
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Chow groups and L-derivatives of automorphic motives for unitary groups, II.
Forum of Mathematics, Pi, 2022 In this article, we improve our main results from [LL21] in two directions: First, we allow ramified places in the CM extension $E/F$ at which we consider representations that are spherical with respect to a certain special maximal compact subgroup, by ...
Chao Li, Yifeng Liu
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Point counting for foliations over number fields
Forum of Mathematics, Pi, 2022 Let${\mathbb M}$ be an affine variety equipped with a foliation, both defined over a number field ${\mathbb K}$. For an algebraic $V\subset {\mathbb M}$ over ${\mathbb K}$, write $\delta _{V}$ for the maximum of the degree and log-height of V.
Gal Binyamini
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Heights on stacks and a generalized Batyrev–Manin–Malle conjecture
Forum of Mathematics, Sigma, 2023 We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties.
Jordan S. Ellenberg +2 more
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Hensel minimality II: Mixed characteristic and a diophantine application
Forum of Mathematics, Sigma, 2023 In this paper, together with the preceding Part I [10], we develop a framework for tame geometry on Henselian valued fields of characteristic zero, called Hensel minimality. It adds to [10] the treatment of the mixed characteristic case.
Raf Cluckers +3 more
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Analytic torsion of Hirzebruch surfaces [PDF]
, 2004 Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch ...
Mourougane, Christophe
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THE EXPLICIT MORDELL CONJECTURE FOR FAMILIES OF CURVES
Forum of Mathematics, Sigma, 2019 In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method bases on some
SARA CHECCOLI +2 more
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Upper bound for the height of S-integral points on elliptic curves [PDF]
, 2012 We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set S of places of the number field K involved, but also in terms of the degree of K, as well as the rank, the ...
Bosser, Vincent, Surroca, Andrea
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SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES
Forum of Mathematics, Sigma, 2018 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.
JOSÉ IGNACIO BURGOS GIL +2 more
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Torsion points with multiplicatively dependent coordinates on elliptic curves
, 2020 In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations.
Barroero, Fabrizio, Sha, Min
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