When: Jan. 15th 2020, 16:00.

Where: Building 108, Room 318.

Speaker: Lee Wan (이완), Yonsei University.

Title: On capitulation map of global fields.

Abstract: For a finite Galois extension L/K of global fields, let C(L) and C(K) denote the Galois groups of maximal S-ramified T-split abelian extensions of L and M, respectively (where S and T are sets of places). There is a natural map Ver from C(K) to C(L) induced from the transfer homomorphism. Since Artin's principal ideal theorem, to determine the kernel and the cokernel of Ver has been an interesting problem. They can be described by Galois cohomology groups of unit groups. As a corollary, we get the strict cohomological dimension of the Galois group of the S-ramified T-split maximal extension of a global field is equal to 2 when S has Dirichlet density 1 and T is finite.

Where: Building 108, Room 318.

Speaker: Lee Wan (이완), Yonsei University.

Title: On capitulation map of global fields.

Abstract: For a finite Galois extension L/K of global fields, let C(L) and C(K) denote the Galois groups of maximal S-ramified T-split abelian extensions of L and M, respectively (where S and T are sets of places). There is a natural map Ver from C(K) to C(L) induced from the transfer homomorphism. Since Artin's principal ideal theorem, to determine the kernel and the cokernel of Ver has been an interesting problem. They can be described by Galois cohomology groups of unit groups. As a corollary, we get the strict cohomological dimension of the Galois group of the S-ramified T-split maximal extension of a global field is equal to 2 when S has Dirichlet density 1 and T is finite.