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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...

Primitive elements in integral bases

Bart de Smit — 1995

Acta Arithmetica

Brauer-Kuroda relations for S-class numbers

Bart de Smit — 2001

Acta Arithmetica

A differential criterion for complete intersections.

Bart De Smit — 1997

Collectanea Mathematica

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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