Nearby cycles for log smooth families |
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| Authors: | Chikara Nakayama |
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| Affiliation: | (1) Department of Mathematics, Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, 152 Tokyo, Japan |
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| Abstract: | 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. |
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| Keywords: | nearby cycle vanishing cycle l-adic cohomology log geometry. |
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