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Nearby cycles for log smooth families

Published online by Cambridge University Press:  04 December 2007

CHIKARA NAKAYAMA
CHIKARA NAKAYAMA
Affiliation:
Tokyo Institute of Technology, Department of Mathematics, Oh-okayama 2-12-1, Meguro-ku, 152 Tokyo, Japan. e-mail: cnakayam@math.titech.ac.jp
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Abstract

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We calculate l-adic nearby cycles in the étale cohomology for families with log smooth reduction using log étale cohomology. In particular, nearby cycles for log smooth families coincide with tame nearby cycles, as L. Illusie expected, and nearby cycles for semistable families depend only on the first infinitesimal neighborhood of the special fiber.

Keywords

nearby cyclevanishing cycle$l$-adic cohomologylog geometry.
Type
Research Article
Information
Compositio Mathematica , Volume 112 , Issue 1 , May 1998 , pp. 45 - 75
Copyright
© 1998 Kluwer Academic Publishers