Algebraic Geometry Seminar

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Date, time & place Tuesday 15:30 - 17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

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2019/01/29

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Kentaro Mitsui (Kobe)
Logarithmic good reduction and the index (TBA)
[ Abstract ]
A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.