Séminaire de Mathématique

Rigid analytic geometry, skeletons, and non-Archimedean integrable systems

by Prof. Andrew Macpherson (Imperial College London & IHÉS)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

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Abstract: The theory of skeletons gives a way to write a non-Archimedean analytic space as fibred generically in tori over a polyhedral complex of (real) dimension equal to that of the analytic space. One does this procedure in the hope that the polyhedral complex can eventually tell us something about the original space. This is a precise version of a still mainly conjectural picture in complex geometry.

I'll give a panoramic overview of the various structures appearing in the subject, the techniques involved in constructing them, and what they can do for us.