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Dergiler / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 4

Swan conductors and torsion in the logarithmic de Rham complex

Sinan ÜNVER

Sayfa
451–464
DOI
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Özet

We prove, for an arithmetic scheme X/S over a discrete valuation ring whose special fiber is a strict normal crossings divisor in X, that the Swan conductor of X/S is equal to the Euler characteristic of the torsion in the logarithmic de Rham complex of X/S. This is a precise logarithmic analog of a theorem by Bloch [1].

Abstract

We prove, for an arithmetic scheme X/S over a discrete valuation ring whose special fiber is a strict normal crossings divisor in X, that the Swan conductor of X/S is equal to the Euler characteristic of the torsion in the logarithmic de Rham complex of X/S. This is a precise logarithmic analog of a theorem by Bloch [1].

Anahtar kelimeler: Turk. J. Math., 34, (2010), 451-464. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.34, iss.4.

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