Cyclotomic units and central extensions of function fields

Abstract

In this paper, we study two topics related to the arithmetic of cyclotomic function field; one is a construction of base for cyclotomic units and the other is central extension and Hasse norm principle. In section 2.1, we construct a base for the universal punctured even distribution. In section 2.2, we obtaine a base for the cyclotomic units. In section 3.1, we introduce genus fields and central extensions over function field and their Galois groups and degrees. In section 3.2, we describe several criterion for the validity of Hasse norm principle. In section 3.3 and 3.4, we characterize the validity of Hasse norm principle for cyclotomic function field and their maximal real subfields. In chapter 4, we investigate l-divisibility of ideal class number of cyclotomic function field and their maximal real subfields.