arXiv subjects

Damian Rössler

Publications and source records attributed to Damian Rössler.

21 records · Page 2Linked to original sources

arXiv2008

On the $p$-adic distance between a point of finite order and a curve of genus higher or equal to two

Let $A$ be an abelian variety over ${\bf C}_p$ ($p$ a prime number) and $V\hookrightarrow A$ a closed subvariety. The conjecture of Tate-Voloch predicts that the $p$-adic distance from a torsion point $T\not\in V({\bf C}_p)$ to the variety $V$ is bounded below by a strictly positive constant. This conjecture is proven by Hrushovski and Scanlon, when $A$ has a model over $\bar{\bf C}_p$. We give an explicit formula for this constant, in the case where $V$ is a curve embedded into its Jacobian and $V$ has a model over a number field. This explicit formula involves analytic and arakelovian invariants of the curve.

math.AG↗

arXiv2008

An arithmetic Riemann-Roch theorem in higher degrees

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

math.AG↗

arXiv2007

On the determinant bundles of abelian schemes

Let $π:\CA\ra S$ be an abelian scheme over a scheme $S$ which is quasi-projective over an affine noetherian scheme and let $\CL$ be a symmetric, rigidified, relatively ample line bundle on $\CA$. We show that there is an isomorphism \det(π_*\CL)^{øtimes 24}\simeq\big(π_*ω_{\CA}^{\vee}\big)^{øtimes 12d} of line bundles on $S$, where $d$ is the rank of the (locally free) sheaf $π_*\CL$. We also show that the numbers 24 and $12d$ are sharp in the following sense: if $N>1$ is a common divisor of 12 and 24, then there are data as above such that \det(π_*\CL)^{øtimes (24/N)}\not\simeq\big(π_*ω_{\CA}^{\vee}\big)^{øtimes (12d/N)}.

math.AG↗