Greenberg's conjecture and units in multiple Zp-extensions
Abstract
In this paper we prove Greenberg's pseudo-null conjecture for the field of p-th roots of unity in the case that p exactly divides the class number and the index of the global units in the local units. We also generalize to the case of multiple Zp-extensions a theorem of Iwasawa on the Kummer extension of the cyclotomic Zp-extension generated by p-power roots of units .
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.