Extensions of Vector Bundles on the Fargues-Fontaine Curve
| Autor: | Christopher Birkbeck, Serin Hong, David T. Hansen, Qirui Li, Lynnelle Ye, Tony Feng, Anthony Wang |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Mathematics - Number Theory General Mathematics 010102 general mathematics Vector bundle Field (mathematics) 16. Peace & justice 01 natural sciences Moduli space Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Simple (abstract algebra) Bundle 0103 physical sciences Euclidean geometry FOS: Mathematics Perfectoid 010307 mathematical physics Number Theory (math.NT) 0101 mathematics Algebraically closed field Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Journal of the Institute of Mathematics of Jussieu |
| Popis: | We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder-Narasimhan polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholze's language of diamonds. This analysis reduces our main results to a somewhat involved combinatorial problem, which we then solve via a reinterpretation in terms of the euclidean geometry of Harder-Narasimhan polygons. 41 pages, 17 figures: Final version; to appear in J Inst. Math. Jussieu |
| Databáze: | OpenAIRE |
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