Zobrazeno 1 - 10
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pro vyhledávání: '"Habegger, Philipp"'
Autor:
Gao, Ziyang, Habegger, Philipp
We prove the Relative Manin-Mumford Conjecture for families of abelian varieties in characteristic 0. We follow the Pila-Zannier method to study special point problems, and we use the Betti map which goes back to work of Masser and Zannier in the cas
Externí odkaz:
http://arxiv.org/abs/2303.05045
Autor:
Gao, Ziyang, Habegger, Philipp
Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in certain m
Externí odkaz:
http://arxiv.org/abs/2303.04936
We consider the set $\mathcal{M}_n(\mathbb Z; H)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain a new upper bound on the number of matrices from $\mathcal{M}_n(\mathbb Z; H)$ with a given characteristic polynomial $f \i
Externí odkaz:
http://arxiv.org/abs/2203.03880
Autor:
Habegger, Philipp, Schmidt, Harry
In a recent breakthrough, Dimitrov solved the Schinzel-Zassenhaus Conjecture. We follow his approach and adapt it to certain dynamical systems arising from polynomials of the form $T^p+c$ where $p$ is a prime number and where the orbit of $0$ is fini
Externí odkaz:
http://arxiv.org/abs/2111.01870
We propose a formulation of the relative Bogomolov conjecture and show that it gives an affirmative answer to a question of Mazur's concerning the uniformity of the Mordell-Lang conjecture for curves. In particular we show that the relative Bogomolov
Externí odkaz:
http://arxiv.org/abs/2009.08505
Let $\alpha \in \mathbb{C}$ be an exponential period. We show that the real and imaginary part of $\alpha$ are up to signs volumes of sets definable in the o-minimal structure generated by $\mathbb{Q}$, the real exponential function and ${\sin}|_{[0,
Externí odkaz:
http://arxiv.org/abs/2007.08280
Consider a smooth, geometrically irreducible, projective curve of genus $g \ge 2$ defined over a number field of degree $d \ge 1$. It has at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the number
Externí odkaz:
http://arxiv.org/abs/2001.10276
Autor:
Dimitrov, Vesselin, Habegger, Philipp
Publikováno v:
Alg. Number Th. 18 (2024) 1945-2001
We prove that the Galois equidistribution of torsion points of the algebraic torus $\mathbb{G}_{m}^d$ extends to the singular test functions of the form $\log{|P|}$, where $P$ is a Laurent polynomial having algebraic coefficients that vanishes on the
Externí odkaz:
http://arxiv.org/abs/1909.06051
Consider a one-parameter family of smooth, irreducible, projective curves of genus $g\ge 2$ defined over a number field. Each fiber contains at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the numb
Externí odkaz:
http://arxiv.org/abs/1904.07268