eprintid: 14833
rev_number: 21
eprint_status: archive
userid: 492
dir: disk0/00/01/48/33
datestamp: 2013-04-18 12:59:16
lastmod: 2013-04-23 10:16:48
status_changed: 2013-04-18 12:59:16
type: doctoralThesis
metadata_visibility: show
creators_name: Sigl, Martin
title: Ramification filtration by moduli in higher-dimensional global class field theory
subjects: ddc-500
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
cterms_swd: Klassenkörpertheorie
abstract: In their approach to higher-dimensional global class field theory, Kato and Saito define the class group of a proper arithmetic scheme \bar{X} as an inverse limit C_{KS}(\bar{X}) = \varprojlim_{\mathcal{I}} C_{\mathcal{I}}(\bar{X}) of certain Nisnevich cohomology groups C_{\mathcal{I}}(\bar{X}) taken over all non-zero coherent ideal sheaves \mathcal{I} of \mathcal{O}_{\bar{X}}.
The ideal sheaves \mathcal{I} should be regarded as higher-dimensional analogues of the classical moduli \mathfrak{m} on a global field K, which induce a filtration of the idele class group C_K  by the ray class groups C_K/C_K^{\mathfrak{m}}.
In higher dimensions however, it is not clear how the induced filtration of the abelian fundamental group can be interpreted in terms of ramification.
In view of Wiesend's class field theory, we define an easier notion of moduli in higher dimensions only involving curves on the scheme. We then show that both notions agree for moduli that correspond to tame ramification.
date: 2013
id_scheme: DOI
id_number: 10.11588/heidok.00014833
ppn_swb: 1652310770
own_urn: urn:nbn:de:bsz:16-heidok-148331
date_accepted: 2013-03-22
advisor: HASH(0x559e37cc1548)
language: eng
bibsort: SIGLMARTINRAMIFICATI2013
full_text_status: public
citation:   Sigl, Martin  (2013) Ramification filtration by moduli in higher-dimensional global class field theory.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/14833/1/CFT.pdf