Bertini theorems and Lefschetz pencils over discrete valuation rings, with applications to higher class field theory

2009/11/07 by Uwe Jannsen, Jannsen, Uwe, Shuji Saito +1 · 1 citation
Computer Science · Mathematics · #11R37 #14G25 #14N05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #math.AG #msc:11R37 #msc:14G25 #msc:14N05

paper · pdf · doi:10.48550/arxiv.0911.1470

19 Pages

arxiv created 2009/11/07 · openalex publication_date 2009/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the existence of good hyperplane sections for schemes over discrete valuation rings with good or (quasi) semistable reduction, and the existence of good Lefschetz pencils for schemes with good reduction or ordinary quadratic reduction. As an application we prove that the reciprocity map introduced for smooth projective varieties over local fields by Bloch, Kato and Saito is an isomorphism after profinite completion, if the variety has good reduction or 'almost good' reduction.

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