## Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Monodromy and Log Geometry

Seminar | October 31 | 3:45-4:45 p.m. | 939 Evans Hall

Arthur Ogus, UC Berkeley

Department of Mathematics

A proper semistable family over a disc gives rise to a smooth proper and saturated morphism $X/S$ of log analytic spaces over the log disc. We will explain how the underlying map of topological spaces $X_{top}/S_{top}$ can be recovered from the restriction $X_0/S_0$ of $X/S$ to the log point. We will also give simple formulas for the action of the monodromy and the differentials on the $E_2$ terms of the “nearby cycles” spectral sequence in terms of the log structure on $X_0/S_0$. This is joint work with Piotr Achinger.

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