On nonemptiness of Newton strata in the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GL}_n$
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913358694842368 |
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| author | Hong, Serin |
| author_facet | Hong, Serin |
| contents | We study the Newton stratification in the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GL}_n$ associated to an arbitrary (possibly nonbasic) element of $B(\mathrm{GL}_n)$. Our main result classifies all nonempty Newton strata in an arbitrary minuscule Schubert cell. For a large class of elements in $B(\mathrm{GL}_n)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08374 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On nonemptiness of Newton strata in the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GL}_n$ Hong, Serin Algebraic Geometry Number Theory We study the Newton stratification in the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GL}_n$ associated to an arbitrary (possibly nonbasic) element of $B(\mathrm{GL}_n)$. Our main result classifies all nonempty Newton strata in an arbitrary minuscule Schubert cell. For a large class of elements in $B(\mathrm{GL}_n)$, 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. |
| title | On nonemptiness of Newton strata in the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GL}_n$ |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2209.08374 |