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

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

2009-11-07

arxiv.org/abs/0911.1470v1

Mathematics

Algebraic Geometry

19 Pages

Scientific paper

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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