Date of Award
Master of Science (MS)
Let F be a totally real number field of degree d and let n >= 2 be an even integer. We denote by W KM2n-2(F) the n-th motivic wild kernel of F, which acts as an analogue to
the class group of F. Assuming the 2-adic Iwasawa Main Conjecture, we prove that the there are only finitely many totally real number fields F having |W KM2n-2(F)| = 1 for some even integer n>=2. In particular we show that there are no totally real number fields having trivial n-th motivic wild kernel for n >= 6, and that there is precisely one totally real number field having trivial 4th motivic wild kernel, namely Q(√(5)). We prove that all totally real number fields having trivial 2nd motivic wild kernel must be of degree d <= 117 (respectively d <= 46 under the assumption of the Generalized Riemann Hypothesis). Using Sage mathematical software, we enumerate all totally real fields of degree d < 10 having trivial 2nd motivic wild kernel, finding 21 such fields. Under restrictions on the local properties of F, we enumerate all relevant fields having trivial 2nd motivic wild kernel.
Junkins, Caroline, "The Analogue of the Gauss Class Number Problem in Motivic Cohomology" (2010). Open Access Dissertations and Theses. Paper 4270.
McMaster University Library