arXiv subjects

Damian Rossler

Publications and source records attributed to Damian Rossler.

2 recordsLinked to original sources

arXiv2009

A note on the ramification of torsion points lying on curves of genus at least two

Let $C$ be a curve of genus $g\geqslant 2$ defined over the fraction field $K$ of a complete discrete valuation ring $R$ with algebraically closed residue field. Suppose that $\char(K)=0$ and that the characteristic of the residue field is not 2. Suppose that the Jacobian $\Jac(C)$ has semi-stable reduction over $R$. Embed $C$ in $\Jac(C)$ using a $K$-rational point. We show that the coordinates of the torsion points lying on $C$ lie in the unique moderately ramified quadratic extension of the field generated over $K$ by the coordinates of the $p$-torsion points on $\Jac(C)$.

math.AG↗

arXiv2005

An afterthought on the generalized Mordell-Lang conjecture

The generalized Mordell-Lang conjecture (GML) is the statement that the irreducible components of the Zariski closure of a subset of a group of finite rank inside a semi-abelian variety are translates of closed algebraic subgroups. M. McQuillan gave a proof of this statement. We revisit his proof, indicating some simplifications. This text contains a complete elementary proof of the fact that (GML) for groups of torsion points (= generalized Manin-Mumford conjecture), together with (GML) for finitely generated groups imply the full generalized Mordell-Lang conjecture.

math.NT↗