Index formulae for integral Galois modules

Details Index formulae for integral Galois modules Index formulae for integral Galois modules

2011-05-19

arxiv.org/abs/1105.3876v3

Mathematics

Number Theory

14 pages; several inaccuracies have been corrected, Corollary 2.8 has been added

Scientific paper

We prove very general index formulae for integral Galois modules, specifically for units in rings of integers of number fields, for higher K-groups of rings of integers, and for Mordell-Weil groups of elliptic curves over number fields. These formulae link the respective Galois module structure to other arithmetic invariants, such as class numbers, or Tamagawa numbers and Tate-Shafarevich groups. This is a generalisation of known results on units to other Galois modules and to many more Galois groups, and at the same time a unification of the approaches hitherto developed in the case of units.

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