Abstract
We show the existence of good hyperplane sections for schemes over discrete valuation rings with good or (quasi-)semi-stable 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 K K by Bloch, Kato and Saito is an isomorphism after ℓ \ell -adic completion, if the variety has good or ordinary quadratic reduction and ℓ ≠ c h a r ( K ) \ell \neq \mathrm {char}(K) .
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