Explicit Coleman integration for hyperelliptic curves
Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman i...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2010
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| _version_ | 1826289993592602624 |
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| author | Balakrishnan, J Bradshaw, R Kedlaya, K |
| author_facet | Balakrishnan, J Bradshaw, R Kedlaya, K |
| author_sort | Balakrishnan, J |
| collection | OXFORD |
| description | Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage. |
| first_indexed | 2024-03-07T02:37:23Z |
| format | Journal article |
| id | oxford-uuid:a93e64ba-1a65-43c7-9c7b-a80fc44523e6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:37:23Z |
| publishDate | 2010 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:a93e64ba-1a65-43c7-9c7b-a80fc44523e62022-03-27T03:07:10ZExplicit Coleman integration for hyperelliptic curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a93e64ba-1a65-43c7-9c7b-a80fc44523e6EnglishSymplectic Elements at OxfordSpringer2010Balakrishnan, JBradshaw, RKedlaya, KColeman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage. |
| spellingShingle | Balakrishnan, J Bradshaw, R Kedlaya, K Explicit Coleman integration for hyperelliptic curves |
| title | Explicit Coleman integration for hyperelliptic curves |
| title_full | Explicit Coleman integration for hyperelliptic curves |
| title_fullStr | Explicit Coleman integration for hyperelliptic curves |
| title_full_unstemmed | Explicit Coleman integration for hyperelliptic curves |
| title_short | Explicit Coleman integration for hyperelliptic curves |
| title_sort | explicit coleman integration for hyperelliptic curves |
| work_keys_str_mv | AT balakrishnanj explicitcolemanintegrationforhyperellipticcurves AT bradshawr explicitcolemanintegrationforhyperellipticcurves AT kedlayak explicitcolemanintegrationforhyperellipticcurves |