Thomas Weigel (19/12/2018)

Valentina Giangreco, desember 13, 2018

Málstofa í stærðfræði

Fyrirlesari: Thomas Weigel, Università di Milano-Bicocca 

Titill: The capitulation kernel and Hilbert’s theorem 94

Staðsetning: VR-II, 158
Tími: Miðvikudagur 11. desember kl. 11.00

Ágrip:

One of the central theorems in Algebraic Number theory
is the finiteness of The capitulation kernel and Hilbert’s theorem 94.

One of the central theorems in Algebraic Number theory
is the finiteness of the Ideal class group of a number field. 
The capitulation kernel k(R/O) is the subgroup of ideal classes which 
become principal under an extension of Dedekind domains R/O. 
Hilbert’s theorem 94 states that for a finite cyclic Galois extension
L/K of number fields of prime power degree, the order of k(R/O) is divisible
by |L:K|. This fact motivated D. Hilbert to formulate his
Principal ideal conjecture which was proved by P. Furtwängler 30 years later.
In this seminar we show a strong version of Hilbert’s theorem 94, which is based
on an abstract version of Hilbert’s theorem 90.f the Ideal class group of a number field. 
The capitulation kernel k(R/O) is the subgroup of ideal classes which 
become principal under an extension of Dedekind domains R/O. 
Hilbert’s theorem 94 states that for a finite cyclic Galois extension
L/K of number fields of prime power degree, the order of k(R/O) is divisible
by |L:K|. This fact motivated D. Hilbert to formulate his
Principal ideal conjecture which was proved by P. Furtwängler 30 years later.
In this seminar we show a strong version of Hilbert’s theorem 94, which is based
on an abstract version of Hilbert’s theorem 90.