Philipp Habegger

activity

20142023

most citedTeichmueller curves in genus three and just likely intersections in

G_{m}^{n} x G_{a}^{n}

7 citations · 10 across the 4 of their papers we have counts for

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3 papers · 1 filter

math.NT2023

Degeneracy loci in the universal family of abelian varieties

Ziyang Gao, Philipp Habegger

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.…

math.NT2016★ 3 cited

Diophantine Approximations on Definable Sets

P. Habegger

Consider the vanishing locus of a real analytic function on $R^{n}$ restricted to $[0, 1]^{n}$ . We bound the number of rational points of bounded height that approximate this s…

math.NT2016

Quasi-equivalence of Heights and Runge's Theorem

P. Habegger

Let $P$ be a polynomial that depends on two variables $X$ and $Y$ and has algebraic coefficients. If $x$ and $y$ are algebraic numbers with $P (x, y) = 0$ , then by work of Néron $h(x)/…