title: Ramification filtration by moduli in higher-dimensional global class field theory
creator: Sigl, Martin
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-510
subject: 510 Mathematics
description: 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
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/14833/1/CFT.pdf
identifier: DOI:10.11588/heidok.00014833
identifier: urn:nbn:de:bsz:16-heidok-148331
identifier:   Sigl, Martin  (2013) Ramification filtration by moduli in higher-dimensional global class field theory.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/14833/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng