Vol. 8, No. 3, 2014

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Lefschetz theorem for abelian fundamental group with modulus

Moritz Kerz and Shuji Saito

Vol. 8 (2014), No. 3, 689–701
Abstract

We prove a Lefschetz hypersurface theorem for abelian fundamental groups allowing wild ramification along some divisor. In fact, we show that isomorphism holds if the degree of the hypersurface is large relative to the ramification along the divisor.

Keywords
fundamental group, ramification, Lefschetz theorem
Mathematical Subject Classification 2010
Primary: 14H30
Secondary: 14E22
Milestones
Received: 27 April 2013
Revised: 12 November 2013
Accepted: 10 December 2013
Published: 31 May 2014
Authors
Moritz Kerz
Naturwissenschaftliche Fakultät I – Mathematik
Universität Regensburg
93040 Regensburg
Germany
Shuji Saito
Interactive Research Center of Science
Graduate School of Science and Engineering
Tokyo Institute of Technology
Ookayama, Meguro
Tokyo 152-8551
Japan