arXiv subjects
Publications and source records attributed to Hendrik Verhoek.
We show that certain abelian varieties over $\Q$ with bad reduction at one prime only are modular by using methods based on the tables of Odlyzko and class field theory.
For a number field $K$, a finite set of primes $S$ not containing a fixed prime $p$, we explain when extensions of group schemes of $μ_p$ by $\Z/p\Z$ split over the ring of $S$-integers $O_S$ of $K$.
Let $A$ be an abelian variety over a number field $K$ with good reduction outside a finite set of primes $S$. We show that if the $\ell$-torsion subgroup schemes $A[\ell^n]$ lie in a certain category of group schemes, then $A[\ell^n]$ does not contain any subgroup schemes that are étale or are of multiplicative type.