Extensions of vector bundles on the Fargues-Fontaine curve II

Hong, Serin

doi:10.48550/arxiv.2203.12838

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2022

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“…Conversely, given such a commutative diagram we apply a result of Chen-Tong [CT22] to observe that α and γ can be adjusted so that β is a minuscule effective modification at ∞. Then we use a previous result of the author [Hon22] to classify all vector bundles E a ′ and E c ′ that fit into such a commutative diagram, and consequently proceed by induction to obtain the desired classification.…”

Section: Outline Of the Proofmentioning

confidence: 99%

On nonemptiness of Newton strata in the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GL}_n$

Hong¹

2022

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We study the Newton stratification in the B + dR -Grassmannian for GLn associated to an arbitrary (possibly nonbasic) element of B(GLn). Our main result classifies all nonempty Newton strata in an arbitrary minuscule Schubert cell. For a large class of elements in B(GLn), our classification is given by some explicit conditions in terms of Newton polygons. For the proof, we proceed by induction on n using a previous result of the author that classifies all extensions of two given vector bundles on the Fargues-Fontaine curve.Contents 14 3.3. An explicit classification of nonempty Newton strata 15 References 20

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Section: Outline Of the Proofmentioning

confidence: 99%