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Abstract
In their approach to higherdimensional 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 nonzero coherent ideal sheaves \mathcal{I} of \mathcal{O}_{\bar{X}}. The ideal sheaves \mathcal{I} should be regarded as higherdimensional 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.
Item Type:  Dissertation 

Supervisor:  Schmidt, Prof. Dr. Alexander 
Date of thesis defense:  22 March 2013 
Date Deposited:  18 Apr 2013 12:59 
Date:  2013 
Faculties / Institutes:  The Faculty of Mathematics and Computer Science > Department of Mathematics 
Subjects:  500 Natural sciences and mathematics 510 Mathematics 
Controlled Keywords:  Klassenkörpertheorie 