VALUES AT s = -1 OF L-FUNCTIONS FOR MULTI-QUADRATIC EXTENSIONS OF NUMBER FIELDS, AND THE FITTING IDEAL OF THE TAME KERNEL

DOI10.1142/S1793042109002183zbMath1261.11075arXiv0708.0817OpenAlexW2962865162MaRDI QIDQ5324323

Jonathan W. Sands

Publication date: 3 August 2009

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.0817

zbMATH Keywords

tame kernelFitting idealStickelberger idealArtin L-functionmulti-quadratic extension

Mathematics Subject Classification ID

Zeta functions and (L)-functions of number fields (11R42) (K)-theory of global fields (11R70) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27)

Cites Work

• Class fields of abelian extensions of \(\mathbb Q\)
• Values of abelian \(L\)-functions at negative integers over totally real fields
• Relations between \(K_2\) and Galois cohomology
• Base change for higher Stickelberger ideals
• \(p\)-adic Abelian Stark conjectures at \(s=1\)
• Galois co-descent for étale wild kernels and capitulation
• Galois descent and \(K_ 2\) of number fields
• A finiteness theorem for K\(_2\) of a number field
• The Iwasawa conjecture for totally real fields
• A Relation Between the 2-Primary Parts of the Main Conjecture and the Birch-Tate-Conjecture
• Values at s = −1 of L -functions for multi-quadratic extensions of number fields and annihilation of the tame kernel
• L-values and the Fitting ideal of the tame kernel for relative quadratic extensions
• Stark's Conjecture and New Stickelberger Phenomena