Classification of quotient bundles on the Fargues–Fontaine curve

• Serin Hong ^[1]
  1. [1] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 2, 2023
• Idioma: inglés
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• Resumen

  • We completely classify all quotient bundles of a given vector bundle on the Fargues–Fontaine curve. As consequences, we have two additional classification results: a complete classification of all vector bundles that are generated by a fixed number of global sections, and a nearly complete classification of subsheaves of a given vector bundle. For the proof, we combine the dimension counting argument for moduli of bundle maps developed in Birkbeck et al. (J Inst Math Jussieu 21:487–532, 2022) with a series of reduction arguments based on some reinterpretation of the classifying conditions.