Authors: Luc Illusie
Publish Date: 2003/09/23
Volume: 112, Issue: 3, Pages: 271-295
Abstract
Let S be the spectrum of a strictly henselian discrete valuation ring with residue characteristic p and Λ=ℤ/ℓνℤ where ℓ is a prime number ≠p and ν is an integer ≥1 For a scheme X of finite type over S and smooth over S along the special fiber X s outside a closed point x we study the vanishing cycles complex RΦΛ and the tame variation mathoprm Varsigma RPhi rm tLambda x rightarrow RGamma xX sRPsi rm tLambda for Σ in the tame inertia group I t In particular we show that if X is regular flat over S of relative dimension n≥1 and Σ is a topological generator of I t then R q ΦΛ x =0 for q≠n and mathoprm Varsigma RnPhi rm tLambda x rightarrow Hn xX sRPsi rm tLambda is an isomorphism
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