Integral differential forms for superelliptic curves.
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| Title: | Integral differential forms for superelliptic curves. |
|---|---|
| Authors: | Kunzweiler, Sabrina1 (AUTHOR), Wewers, Stefan2 (AUTHOR) |
| Source: | Mathematics of Computation. Sep2026, Vol. 95 Issue 361, p2559-2593. 35p. |
| Subjects: | Differential forms, Local fields (Algebra), Algorithms, Elliptic curves, Mathematics, Algebraic geometry, Mathematical singularities, Scientific models |
| Abstract: | Given a superelliptic curve Y_K:\; y^n=f(x) over a local field K, we describe the theoretical background and an implementation of a new algorithm for computing the \mathfrak {o}_K-lattice of integral differential forms on Y_K. We build on the results of Obus and Wewers [J. Algebraic Geom. 29 (2020), pp. 691–728] who describe arbitrary regular models of the projective line using only valuations. One novelty of our approach is that we construct an \mathfrak {o}_K-model of Y_K with only rational singularities, but which may not be regular. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Computation is the property of American Mathematical Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194543854 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Integral differential forms for superelliptic curves. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kunzweiler%2C+Sabrina%22">Kunzweiler, Sabrina</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wewers%2C+Stefan%22">Wewers, Stefan</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Computation%22">Mathematics of Computation</searchLink>. Sep2026, Vol. 95 Issue 361, p2559-2593. 35p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Differential+forms%22">Differential forms</searchLink><br /><searchLink fieldCode="DE" term="%22Local+fields+%28Algebra%29%22">Local fields (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+curves%22">Elliptic curves</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+geometry%22">Algebraic geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+models%22">Scientific models</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Given a superelliptic curve Y_K:\; y^n=f(x) over a local field K, we describe the theoretical background and an implementation of a new algorithm for computing the \mathfrak {o}_K-lattice of integral differential forms on Y_K. We build on the results of Obus and Wewers [J. Algebraic Geom. 29 (2020), pp. 691–728] who describe arbitrary regular models of the projective line using only valuations. One novelty of our approach is that we construct an \mathfrak {o}_K-model of Y_K with only rational singularities, but which may not be regular. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Computation is the property of American Mathematical Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1090/mcom/4115 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 2559 Subjects: – SubjectFull: Differential forms Type: general – SubjectFull: Local fields (Algebra) Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Elliptic curves Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Algebraic geometry Type: general – SubjectFull: Mathematical singularities Type: general – SubjectFull: Scientific models Type: general Titles: – TitleFull: Integral differential forms for superelliptic curves. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kunzweiler, Sabrina – PersonEntity: Name: NameFull: Wewers, Stefan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00255718 Numbering: – Type: volume Value: 95 – Type: issue Value: 361 Titles: – TitleFull: Mathematics of Computation Type: main |
| ResultId | 1 |
