cicyt UNIZAR
Full-text links:

Download:

Current browse context:

math.NT

Change to browse by:

References & Citations

Bookmark

(what is this?)
CiteULike logo BibSonomy logo Mendeley logo del.icio.us logo Digg logo Reddit logo ScienceWISE logo

Mathematics > Number Theory

Title: On the Iwasawa asymptotic class number formula for $\mathbb{Z}_p^r\rtimes\mathbb{Z}_p$-extensions

Abstract: Let $p$ be an odd prime and $F_{\infty,\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group isomorphic to $\mathbb{Z}_p^r\rtimes\mathbb{Z}_p$, $r\geq 1$. Under certain assumptions, we prove an asymptotic formula for the growth of $p$-exponents of the class groups in the said $p$-adic Lie extension. This generalizes a previous result of Lei, where he establishes such a formula in the case $r=1$. An important and new ingredient towards extending Lei's result rests on an asymptotic formula for a finitely generated (not necessarily torsion) $\mathbb{Z}_p[[\mathbb{Z}_p^r]]$-module which we will also establish in this paper. We then continue studying the growth of $p$-exponents of the class groups under more restrictive assumptions and show that there is an asymptotic formula in our noncommutative $p$-adic Lie extension analogous to a refined formula of Monsky (which is for the commutative extension) in a special case.
Comments: 17 pages
Subjects: Number Theory (math.NT)
Cite as: arXiv:1803.06095 [math.NT]
  (or arXiv:1803.06095v1 [math.NT] for this version)

Submission history

From: Meng Fai Lim [view email]
[v1] Fri, 16 Mar 2018 07:12:54 GMT (16kb)