2024/03/12 by Efrat, Ido · 1 citation
#12G05 #12J10 #FOS: Mathematics #Number Theory (math.NT) #Primary 11R32 #Secondary 11R34
paper · doi:10.48550/arxiv.2403.07482
The mod-2 arithmetic Milnor invariants, introduced by Morishita, provide a decomposition law for primes in canonical Galois extensions of ℚ with unitriangular Galois groups, and contain the Legendre and Redei symbols as special cases. Morishita further proposed a notion of mod-q arithmetic Milnor invariants, where q is a prime power, for number fields containing the q-th roots of unity and satisfying certain class field theory assumptions. We extend this theory from the number field context to general fields, by introducing a notion of a linking invariant for discrete valuations and orderings. We further express it as a Magnus homomorphism coefficient, and relate it to Massey product elements in Galois cohomology.