On p-adic vanishing cycles of log smooth families
Copyright policy )On p-adic vanishing cycles of log smooth families
In this paper, we will show that the sheaf of p-adic vanishing cycles of a log smooth family over a DVR of mixed characteristic is generated by Milnor symboles. A key ingredient is a computation (due to K. Kato) on the graded quotients of a multi-indexed filtration on the sheaf concerned, which has been used in several papers of the first author.
26 pages. Setions 5 and 6 are reorganized, and typos have been fixed
- University of Tokyo Japan
- Mie Chukyo University Japan
Milnor $K$-groups, 14F20, Milnor \(K\)-groups, Mathematics - Number Theory, 11G45, \(p\)-adic cohomology, crystalline cohomology, 14F30, log smooth families, $p$-adic vanishing cycles, Étale and other Grothendieck topologies and (co)homologies, 14F20, 11G99, FOS: Mathematics, Geometric class field theory, Number Theory (math.NT), \(p\)-adic vanishing cycles
Milnor $K$-groups, 14F20, Milnor \(K\)-groups, Mathematics - Number Theory, 11G45, \(p\)-adic cohomology, crystalline cohomology, 14F30, log smooth families, $p$-adic vanishing cycles, Étale and other Grothendieck topologies and (co)homologies, 14F20, 11G99, FOS: Mathematics, Geometric class field theory, Number Theory (math.NT), \(p\)-adic vanishing cycles
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