Academic Journal
De Rham [InlineEquation not available: see fulltext.]-factors.
| Τίτλος: | De Rham [InlineEquation not available: see fulltext.]-factors. |
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| Συγγραφείς: | Patel, Deepam |
| Πηγή: | Inventiones Mathematicae; Nov2012, Vol. 190 Issue 2, p299-355, 57p |
| Θεματικοί όροι: | EPSILON (Computer program language), Cohomology theory, Equations, Curves, Mathematics |
| Περίληψη: | We construct a theory of de Rham epsilon factors. Given a smooth projective variety X over a field of characteristic 0 and a [InlineEquation not available: see fulltext.]-module [InlineEquation not available: see fulltext.], we may consider the determinant of de Rham cohomology [InlineEquation not available: see fulltext.] as a graded super line. Let S be the singular support of [InlineEquation not available: see fulltext.], U an open in X, Y= X∖ U, and ν a 1-form on U⊂ X such that ν( U)∩ S=∅. Then we show the existence of a canonically defined graded super line [InlineEquation not available: see fulltext.] canonically isomorphic to [InlineEquation not available: see fulltext.]. The key property is the local nature of the epsilon factor: it only depends on the restriction of [InlineEquation not available: see fulltext.] and ν to any open neighborhood of Y. Restricting to the case of curves gives a theory of epsilon factors for curves previously defined by Beilinson, Bloch, Deligne, and Esnault. [ABSTRACT FROM AUTHOR] |
| Copyright of Inventiones Mathematicae is the property of Springer Nature 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.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1007/s00222-012-0381-8 Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer |
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| Header | DbId: edb DbLabel: Complementary Index An: 82305699 RelevancyScore: 834 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 834.351501464844 |
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| Items | – Name: Title Label: Title Group: Ti Data: De Rham [InlineEquation not available: see fulltext.]-factors. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Patel%2C+Deepam%22">Patel, Deepam</searchLink> – Name: TitleSource Label: Source Group: Src Data: Inventiones Mathematicae; Nov2012, Vol. 190 Issue 2, p299-355, 57p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22EPSILON+%28Computer+program+language%29%22">EPSILON (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Cohomology+theory%22">Cohomology theory</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink><br /><searchLink fieldCode="DE" term="%22Curves%22">Curves</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We construct a theory of de Rham epsilon factors. Given a smooth projective variety X over a field of characteristic 0 and a [InlineEquation not available: see fulltext.]-module [InlineEquation not available: see fulltext.], we may consider the determinant of de Rham cohomology [InlineEquation not available: see fulltext.] as a graded super line. Let S be the singular support of [InlineEquation not available: see fulltext.], U an open in X, Y= X∖ U, and ν a 1-form on U⊂ X such that ν( U)∩ S=∅. Then we show the existence of a canonically defined graded super line [InlineEquation not available: see fulltext.] canonically isomorphic to [InlineEquation not available: see fulltext.]. The key property is the local nature of the epsilon factor: it only depends on the restriction of [InlineEquation not available: see fulltext.] and ν to any open neighborhood of Y. Restricting to the case of curves gives a theory of epsilon factors for curves previously defined by Beilinson, Bloch, Deligne, and Esnault. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Inventiones Mathematicae is the property of Springer Nature 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: 10.1007/s00222-012-0381-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 57 StartPage: 299 Subjects: – SubjectFull: EPSILON (Computer program language) Type: general – SubjectFull: Cohomology theory Type: general – SubjectFull: Equations Type: general – SubjectFull: Curves Type: general – SubjectFull: Mathematics Type: general Titles: – TitleFull: De Rham [InlineEquation not available: see fulltext.]-factors. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Patel, Deepam IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2012 Type: published Y: 2012 Identifiers: – Type: issn-print Value: 00209910 Numbering: – Type: volume Value: 190 – Type: issue Value: 2 Titles: – TitleFull: Inventiones Mathematicae Type: main |
| ResultId | 1 |