Geodesics between algebraic models via Berkovich geometry

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• Rémi Reboulet, University of Cambridge
• Wednesday 25 May 2022, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Dhruv Ranganathan.

To a projective variety over a non-Archimedean field, one can associate a topological space, its Berkovich analytification Xan, which nicely and compactly organizes the data of models (or degenerations) of X. More generally, if L is for example an ample line bundle on X, one can encode a degeneration of (X,L) as a metric on the Berkovich line bundle L^an. In this talk I explain some basics of Berkovich geometry, and how one can do geometric analysis in such spaces of degenerations, for example by giving them metric structures and constructing geodesic segments.

This talk is part of the Algebraic Geometry Seminar series.

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