Linsheng Yin

INDEX-CLASS NUMBER FORMULAS OVER GLOBAL FUNCTION FIELDS

In classical number theory, one has the famous theorem of Kummer–Sinnott giving the index of the cyclotomic units in the total unit group. Using the division values of sgn-normalized rank one Drinfeld modules, we construct the group of extended cyclotomic units for an abelian extension of a global function field and calculate its index in the whole unit group. The result could be regarded as an analogue and a generalization of Kummer–Sinnotts.

A note on Rubin’s methods of the use of two Euler systems

Here we show that Rubin’s method of the use of two Euler systems to the proofs of Iwasawa main conjectures of the rational number field and of an imaginary quadratic field is only proper to these two kinds of number fields. We mainly use the properties of adéle ring and idéle group in class field theory to get the result.