Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic
Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are a few explicit examples of stratifications. The main goal of this paper is to construct stratifications on projective or affine curves in positive charact...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210224 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic / M. van der Put // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862643572150370304 |
|---|---|
| author | van der Put, M. |
| author_facet | van der Put, M. |
| citation_txt | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic / M. van der Put // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are a few explicit examples of stratifications. The main goal of this paper is to construct stratifications on projective or affine curves in positive characteristic and to determine the possibilities for their differential Galois groups. For the related "differential Abhyankar conjecture", we present partial answers, supplementing the literature. The tools for the construction of regular singular stratifications and the study of their differential Galois groups are p-adic methods and rigid analytic methods using Mumford curves and Mumford groups. These constructions produce many stratifications and differential Galois groups. In particular, some information on the tame fundamental groups of affine curves is obtained.
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| first_indexed | 2025-12-07T21:24:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210224 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:48Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | van der Put, M. 2025-12-04T13:02:09Z 2019 Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic / M. van der Put // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14F10; 13N10; 14G22; 14H30 arXiv: 1812.02965 https://nasplib.isofts.kiev.ua/handle/123456789/210224 https://doi.org/10.3842/SIGMA.2019.071 Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are a few explicit examples of stratifications. The main goal of this paper is to construct stratifications on projective or affine curves in positive characteristic and to determine the possibilities for their differential Galois groups. For the related "differential Abhyankar conjecture", we present partial answers, supplementing the literature. The tools for the construction of regular singular stratifications and the study of their differential Galois groups are p-adic methods and rigid analytic methods using Mumford curves and Mumford groups. These constructions produce many stratifications and differential Galois groups. In particular, some information on the tame fundamental groups of affine curves is obtained. We thank Andreas Maurischat for pointing out that his thesis contains a negative answer to Question 1.2. Many thanks are due to the referees for their work, which is the basis for a major revision of the text. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic Article published earlier |
| spellingShingle | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic van der Put, M. |
| title | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic |
| title_full | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic |
| title_fullStr | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic |
| title_full_unstemmed | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic |
| title_short | Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic |
| title_sort | stratified bundles on curves and differential galois groups in positive characteristic |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210224 |
| work_keys_str_mv | AT vanderputm stratifiedbundlesoncurvesanddifferentialgaloisgroupsinpositivecharacteristic |