Extensions of vector bundles on the Fargues–Fontaine curve II
Author:
Serin Hong
Journal:
J. Algebraic Geom.
DOI:
https://doi.org/10.1090/jag/831
Published electronically:
April 26, 2024
Full-text PDF
Abstract |
References |
Additional Information
Abstract: Given two arbitrary vector bundles on the Fargues–Fontaine curve, we completely classify all vector bundles which arise as their extensions.
References
- Christopher Birkbeck, Tony Feng, David Hansen, Serin Hong, Qirui Li, Anthony Wang, and Lynnelle Ye, Extensions of vector bundles on the Fargues-Fontaine curve, J. Inst. Math. Jussieu 21 (2022), no. 2, 487–532. MR 4386821, DOI 10.1017/S1474748020000183
- Miaofen Chen and Jilong Tong, Weakly admissible locus and Newton stratification in $p$-adic Hodge theory, Amer. J. Math., to appear.
- Laurent Fargues and Jean-Marc Fontaine, Courbes et fibrés vectoriels en théorie de Hodge $p$-adique, Astérisque 406 (2018), xiii+382 (French, with English and French summaries). With a preface by Pierre Colmez. MR 3917141
- Laurent Fargues and Peter Scholze, Geometrization of the local Langlands correspondence, arXiv:2102.13459v3, 2024.
- Serin Hong, On certain extensions of vector bundles in $p$-adic geometry, Math. Res. Lett., to appear.
- Serin Hong, Classification of subbundles on the Fargues-Fontaine curve, Algebra Number Theory 15 (2021), no. 5, 1127–1156. MR 4283099, DOI 10.2140/ant.2021.15.1127
- Serin Hong, On nonemptiness of Newton strata in the ${B}^+_\text {dR}$-Grassmannian for $\mathrm {GL}_n$, arXiv:2209.08374v1, 2022.
- Serin Hong, Classification of quotient bundles on the Fargues-Fontaine curve, Selecta Math. (N.S.) 29 (2023), no. 2, Paper No. 20, 49. MR 4540839, DOI 10.1007/s00029-022-00819-6
- Urs Hartl and Richard Pink, Vector bundles with a Frobenius structure on the punctured unit disc, Compos. Math. 140 (2004), no. 3, 689–716. MR 2041777, DOI 10.1112/S0010437X03000216
- Kiran S. Kedlaya, Slope filtrations revisited, Doc. Math. 10 (2005), 447–525. MR 2184462
- Bhargav Bhatt, Ana Caraiani, Kiran S. Kedlaya, and Jared Weinstein, Perfectoid spaces, Mathematical Surveys and Monographs, vol. 242, American Mathematical Society, Providence, RI, 2019. Lectures from the 2017 Arizona Winter School, held in Tucson, AZ, March 11–17; Edited and with a preface by Bryden Cais; With an introduction by Peter Scholze. MR 3970252, DOI 10.1090/surv/242
- Kiran S. Kedlaya and Ruochuan Liu, Relative $p$-adic Hodge theory: foundations, Astérisque 371 (2015), 239 (English, with English and French summaries). MR 3379653
- Kieu Hieu Nguyen and Eva Viehmann, A Harder-Narasimhan stratification of the $B^+_\textrm {dR}$-Grassmannian, Compos. Math. 159 (2023), no. 4, 711–745. MR 4568424, DOI 10.1112/s0010437x23007066
- Enrico Schlesinger, Extensions of vector bundles on ${\Bbb P}^1$, Comm. Algebra 28 (2000), no. 12, 5883–5889. Special issue in honor of Robin Hartshorne. MR 1808609, DOI 10.1080/00927870008827194
- Xu Shen, Harder-Narasimhan strata and $p$-adic period domains, Trans. Amer. Math. Soc. 376 (2023), no. 5, 3319–3376. MR 4577333, DOI 10.1090/tran/8859
- Peter Scholze and Jared Weinstein, Berkeley lectures on $p$-adic geometry, Annals of Mathematics Studies, vol. 207, Princeton University Press, Princeton, NJ, 2020. MR 4446467
- Eva Viehmann, On Newton strata in the ${B}^+_\text {dR}$-Grassmannian, Duke Math. J. 173 (2024), no. 1, 177–225.
References
- Christopher Birkbeck, Tony Feng, David Hansen, Serin Hong, Qirui Li, Anthony Wang, and Lynnelle Ye, Extensions of vector bundles on the Fargues-Fontaine curve, J. Inst. Math. Jussieu 21 (2022), no. 2, 487–532. MR 4386821, DOI 10.1017/S1474748020000183
- Miaofen Chen and Jilong Tong, Weakly admissible locus and Newton stratification in $p$-adic Hodge theory, Amer. J. Math., to appear.
- Laurent Fargues and Jean-Marc Fontaine, Courbes et fibrés vectoriels en théorie de Hodge $p$-adique, Astérisque 406 (2018), xiii+382 (French, with English and French summaries). With a preface by Pierre Colmez. MR 3917141
- Laurent Fargues and Peter Scholze, Geometrization of the local Langlands correspondence, arXiv:2102.13459v3, 2024.
- Serin Hong, On certain extensions of vector bundles in $p$-adic geometry, Math. Res. Lett., to appear.
- Serin Hong, Classification of subbundles on the Fargues-Fontaine curve, Algebra Number Theory 15 (2021), no. 5, 1127–1156. MR 4283099, DOI 10.2140/ant.2021.15.1127
- Serin Hong, On nonemptiness of Newton strata in the ${B}^+_\text {dR}$-Grassmannian for $\mathrm {GL}_n$, arXiv:2209.08374v1, 2022.
- Serin Hong, Classification of quotient bundles on the Fargues-Fontaine curve, Selecta Math. (N.S.) 29 (2023), no. 2, Paper No. 20, 49. MR 4540839, DOI 10.1007/s00029-022-00819-6
- Urs Hartl and Richard Pink, Vector bundles with a Frobenius structure on the punctured unit disc, Compos. Math. 140 (2004), no. 3, 689–716. MR 2041777, DOI 10.1112/S0010437X03000216
- Kiran S. Kedlaya, Slope filtrations revisited, Doc. Math. 10 (2005), 447–525. MR 2184462
- Bhargav Bhatt, Ana Caraiani, Kiran S. Kedlaya, and Jared Weinstein, Perfectoid spaces, Mathematical Surveys and Monographs, vol. 242, American Mathematical Society, Providence, RI, 2019. Lectures from the 2017 Arizona Winter School, held in Tucson, AZ, March 11–17; Edited and with a preface by Bryden Cais; With an introduction by Peter Scholze. MR 3970252, DOI 10.1090/surv/242
- Kiran S. Kedlaya and Ruochuan Liu, Relative $p$-adic Hodge theory: foundations, Astérisque 371 (2015), 239 (English, with English and French summaries). MR 3379653
- Kieu Hieu Nguyen and Eva Viehmann, A Harder-Narasimhan stratification of the $B^+_{\mathrm {dR}}$-Grassmannian, Compos. Math. 159 (2023), no. 4, 711–745. MR 4568424, DOI 10.1112/s0010437x23007066
- Enrico Schlesinger, Extensions of vector bundles on ${\mathbb {P}}^1$, Comm. Algebra 28 (2000), no. 12, 5883–5889. Special issue in honor of Robin Hartshorne. MR 1808609, DOI 10.1080/00927870008827194
- Xu Shen, Harder-Narasimhan strata and $p$-adic period domains, Trans. Amer. Math. Soc. 376 (2023), no. 5, 3319–3376. MR 4577333, DOI 10.1090/tran/8859
- Peter Scholze and Jared Weinstein, Berkeley lectures on $p$-adic geometry, Annals of Mathematics Studies, vol. 207, Princeton University Press, Princeton, NJ, 2020. MR 4446467
- Eva Viehmann, On Newton strata in the ${B}^+_\text {dR}$-Grassmannian, Duke Math. J. 173 (2024), no. 1, 177–225.
Additional Information
Serin Hong
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721
MR Author ID:
1301698
ORCID:
0000-0002-0410-9041
Email:
serinh@math.arizona.edu
Received by editor(s):
April 13, 2023
Received by editor(s) in revised form:
November 28, 2023
Published electronically:
April 26, 2024
Article copyright:
© Copyright 2024
University Press, Inc.
