Classification of quotient bundles on the Fargues-Fontaine curve

Abstract

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 subbundles of a given vector bundle. For the proof, we combine the dimension counting argument for moduli of bundle maps developed in [BFH+17] with a series of reduction arguments based on some reinterpretation of the classifying conditions.

Figures (13)

• Figure 1: Illustration of the condition \ref{['dual strong slopewise dominance for quotients, intro']} in Theorem \ref{['classification of quotient bundles, intro']}.
• Figure 2: Illustration of the condition \ref{['strong slopewise dominance for subbundles, intro']} in Corollary \ref{['almost classification of subbundles, intro']}.
• Figure 3: Illustration of the condition \ref{['dual strong slopewise dominance for quotients']} in Theorem \ref{['classification of quotient bundles']}.
• Figure 4: Illustration of the condition \ref{['strong slopewise dominance for subbundles']} in Corollary \ref{['almost classification of subbundles']}.
• Figure 5: Illustration of Definition \ref{['def of slopewise dominance']}

Theorems & Definitions (133)

• Theorem 1.1.1: Fargues-Fontaine FF_curve, Kedlaya Kedlaya_slopefiltrations_revisited
• Theorem 1.1.2
• Corollary 1.1.3
• Corollary 1.1.4
• Theorem 1.2.1: Hong_extvb
• Theorem 1.2.2: Hong_subvb
• Definition 2.1.1
• Remark
• Proposition 2.1.2: Kedlaya_noeth
• Remark