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Clemens–Schmid exact sequence in characteristic \(p\)

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Abstract

For a semistable family of varieties over a curve in characteristic \(p\), we prove the existence of a “Clemens–Schmid type” long exact sequence for the \(p\)-adic cohomology. The cohomology groups appearing in such a long exact sequence are defined locally.

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Acknowledgments

We would like to thank A. Shiho and A. Lauder. Lauder’s article [15] was the starting point for this article. The first author was supported by Cariparo Eccellenza Grant “Differential methods in algebra, geometry and arithmetic” and was also supported by a JSPS grant. The second author was supported by a JSPS Grant-in-Aid for research (B) 22340001. We thank Frank Sullivan. We thank the referee for useful remarks.

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Authors and Affiliations

  1. Dip. Matematica, Univ. Padova, Via Trieste 63, 35121 , Padova, Italy

    Bruno Chiarellotto

  2. Mathematical Inst., Tohoku Univ., 6-3, Aoba, Aramaki, Aoba-Ku, Sendai, 980-8578, Japan

    Nobuo Tsuzuki

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  1. Bruno Chiarellotto
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  2. Nobuo Tsuzuki
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Correspondence to Nobuo Tsuzuki.

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Chiarellotto, B., Tsuzuki, N. Clemens–Schmid exact sequence in characteristic \(p\) . Math. Ann. 358, 971–1004 (2014). https://doi.org/10.1007/s00208-013-0980-8

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  • DOI: https://doi.org/10.1007/s00208-013-0980-8

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