Higher Stickelberger ideals and even 𝐾-groups

Abstract

We use the analogy between class groups and even K K -groups of the ring of integers of a number field and “Higher Stickelberger” ideals within K K -theory to prove an index formula for these ideals in a finite abelian extension of real number fields, which is similar to the classic Stickelberger ideal index formula proved by Iwasawa.

On a Gross conjecture over imaginary quadratic fields

“…Their applications in this case are many and touch various subjects in the number theory of higher algebraic K-groups (e.g. [17], [8], [9] and others). In the non-absolute abelian case, Gross's conjecture doesn't provide any particular formula for the definition of these special units.…”