3:45PM: Monodromy and Log Geometry
Arthur OgusA 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 Xtop=Stop can be recovered from the restriction X0=S0 of X=S to the log point. We will also give simple formulas for the action of the monodromy and the dierentials on the E2 terms of the \nearby cycles" spectral sequence in terms of the log structure on X0=S0. This is joint work with Piotr Achinger.