Having the same wild ramification is preserved by the direct image

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Abstract

Let S be the spectrum of an excellent henselian discrete valuation ring of residue characteristic p and X a separated scheme over S of finite type. Let \(\Lambda \) and \(\Lambda '\) be finite fields of characteristics \(\ell \ne p\) and \(\ell '\ne p\) respectively. For elements \(\mathcal {F}\in K_{c}(X,\Lambda )\) and \(\mathcal {F}'\in K_{c}(X,\Lambda ')\) of the Grothendieck groups of the categories of constructible sheaves of \(\Lambda \)-modules and \(\Lambda '\)-modules on X respectively, we introduce the notion that \(\mathcal {F}\) and \(\mathcal {F}'\) have the same wild ramification and prove that this condition is preserved by four of Grothendieck’s six operations except the derived tensor product and \(R \mathcal {H}om\).

Mathematics Subject Classification

Primary 14F20 Secondary 14E22 

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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of TokyoTokyoJapan

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