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Dual pairs of algebras and finite commutative group schemes
Peter Bruin
We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a…
Strongly modular models of -curves
Peter Bruin, Andrea Ferraguti
Let be a -curve without complex multiplication. We address the problem of deciding whether is geometrically isomorphic to a strongly modular -curve. W…
A criterion to rule out torsion groups for elliptic curves over number fields
Peter Bruin, Filip Najman
We present a criterion for proving that certain groups of the form do not occur as the torsion subgroup of any elliptic curve over…
The growth of the rank of Abelian varieties upon extensions
Peter Bruin, Filip Najman
We study the growth of the rank of elliptic curves and, more generally, Abelian varieties upon extensions of number fields. First, we show that if is a finite Galois extensio…
Explicit bounds on canonical Green functions of modular curves
Peter Bruin
We prove explicit bounds on canonical Green functions of Riemann surfaces obtained as compactifications of quotients of the upper half-plane by Fuchsian groups.