Torsion Galois modules and Stickelberger's theoremSpeaker:Luca Caputo (Limoges)
Time: 4.00 PM
Date: Thursday November 22nd 2012
Location: Mathematics Seminar Room, Room AG 1.01, First Floor, Agriculture Building, UCD Belfield
Let G be a finite group and let N/E be a G-Galois tamely ramified extension of number fields. We show how Stickelberger's factorization of Gauss sums implies the stable freeness of various arithmetic Z[G]-modules attached to N/E. More precisely, if O_N denotes the ring of integers of N, we prove that the tensor of O_N with itself over O_E has trivial class in the class group Cl(Z[G]). If N/E is also assumed to be locally abelian, the technique we employ also shows that the inverse different of N/E and its square root (when it exists) define the same class as O_N. This is joint work with S. Vinatier.