UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

December 09, 2008

939 Evans Hall

3:45PM: Tropicalization and nonarchimedean analytification

Sam Payne

Tropicalization is a functor that maps subvarieties of toric varieties over nonarchimedean fields to combinatorial spaces stratified by polyhedral complexes, and may be thought of roughly as taking the image of the variety under the valuation. Analytification is a functor that maps a variety over a nonarchimedean field to a topological space whose points are equivalence classes of multiplicative seminorms on coordinate rings of affine open subsets. I will give a gentle and elementary introduction to these two functors, together with a proof that the analytification of a quasiprojective variety is the inverse limit of the tropicalizations of its closed embeddings in toric varieties.

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