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Nearby cycles for log smooth families

Published online by Cambridge University Press:  04 December 2007

CHIKARA NAKAYAMA
Affiliation:
Tokyo Institute of Technology, Department of Mathematics, Oh-okayama 2-12-1, Meguro-ku, 152 Tokyo, Japan. e-mail: [email protected]
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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.

Type
Research Article
Copyright
© 1998 Kluwer Academic Publishers