Let $K$ be a local field of residue characteristic $p$. Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to-$p$ rational torsion subgroup on the . . .

The period of a curve is the smallest positive degree of Galoisinvariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and index over certain number fi . . .

We present three results on the period-index problem for genus-one curves over global fields. Our first result implies that for every pair of positive integers (P, I) such that I is divisible by P and divides P 2 , there exists a number field K and a . . .