Superspecial curves of genus 4 in small characteristic.
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| Title: | Superspecial curves of genus 4 in small characteristic. |
|---|---|
| Authors: | Kudo, Momonari1 m-kudo@math.kyushu-u.ac.jp, Harashita, Shushi2 harasita@ynu.ac.jp |
| Source: | Finite Fields & Their Applications. May2017, Vol. 45, p131-169. 39p. |
| Subjects: | Arbitrary constants, Mathematical constants, Algebra software, Macsyma (Computer software), Uniqueness (Mathematics) |
| Abstract: | This paper contains a complete study of superspecial curves of genus 4 in characteristic p ≤ 7 . We prove that there does not exist a superspecial curve of genus 4 in characteristic 7. This is a negative answer to the genus 4 case of the problem proposed by Ekedahl [9] in 1987. This implies the non-existence of maximal curve of genus 4 over F 49 , which updates the table at manypoints.org . We give an algorithm to enumerate superspecial nonhyperelliptic curves in arbitrary p ≥ 5 , and for p ≤ 7 we execute it with our implementation on a computer algebra system Magma. Our result in p = 5 re-proves the uniqueness of maximal curves of genus 4 over F 25 , see [11] for the original theoretical proof. In Appendix, we present a general method determining Hasse–Witt matrices of curves which are complete intersections. [ABSTRACT FROM AUTHOR] |
| Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. 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: 122311559 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Superspecial curves of genus 4 in small characteristic. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kudo%2C+Momonari%22">Kudo, Momonari</searchLink><relatesTo>1</relatesTo><i> m-kudo@math.kyushu-u.ac.jp</i><br /><searchLink fieldCode="AR" term="%22Harashita%2C+Shushi%22">Harashita, Shushi</searchLink><relatesTo>2</relatesTo><i> harasita@ynu.ac.jp</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Finite+Fields+%26+Their+Applications%22">Finite Fields & Their Applications</searchLink>. May2017, Vol. 45, p131-169. 39p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Arbitrary+constants%22">Arbitrary constants</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+constants%22">Mathematical constants</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra+software%22">Algebra software</searchLink><br /><searchLink fieldCode="DE" term="%22Macsyma+%28Computer+software%29%22">Macsyma (Computer software)</searchLink><br /><searchLink fieldCode="DE" term="%22Uniqueness+%28Mathematics%29%22">Uniqueness (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper contains a complete study of superspecial curves of genus 4 in characteristic p ≤ 7 . We prove that there does not exist a superspecial curve of genus 4 in characteristic 7. This is a negative answer to the genus 4 case of the problem proposed by Ekedahl [9] in 1987. This implies the non-existence of maximal curve of genus 4 over F 49 , which updates the table at manypoints.org . We give an algorithm to enumerate superspecial nonhyperelliptic curves in arbitrary p ≥ 5 , and for p ≤ 7 we execute it with our implementation on a computer algebra system Magma. Our result in p = 5 re-proves the uniqueness of maximal curves of genus 4 over F 25 , see [11] for the original theoretical proof. In Appendix, we present a general method determining Hasse–Witt matrices of curves which are complete intersections. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. 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: 10.1016/j.ffa.2016.12.001 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 39 StartPage: 131 Subjects: – SubjectFull: Arbitrary constants Type: general – SubjectFull: Mathematical constants Type: general – SubjectFull: Algebra software Type: general – SubjectFull: Macsyma (Computer software) Type: general – SubjectFull: Uniqueness (Mathematics) Type: general Titles: – TitleFull: Superspecial curves of genus 4 in small characteristic. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kudo, Momonari – PersonEntity: Name: NameFull: Harashita, Shushi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2017 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 10715797 Numbering: – Type: volume Value: 45 Titles: – TitleFull: Finite Fields & Their Applications Type: main |
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