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The cyclic subfield integer index

Bart de Smit — 2000

Journal de théorie des nombres de Bordeaux

In this note we consider the index in the ring of integers of an abelian extension of a number field K of the additive subgroup generated by integers which lie in subfields that are cyclic over K . This index is finite, it only depends on the Galois group and the degree of K , and we give an explicit combinatorial formula for it. When generalizing to more general Dedekind domains, a correction term can be needed if there is an inseparable extension of residue fields. We identify this correction term...

Relations between jacobians of modular curves of level p 2

Imin Chen;  Bart De Smit;  Martin Grabitz — 2004

Journal de Théorie des Nombres de Bordeaux

We derive a relation between induced representations on the group GL 2 ( ℤ / p 2 ℤ ) which implies a relation between the jacobians of certain modular curves of level p 2 . The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of GL 2 ( ℤ / p 2 ℤ ) .

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