Chow motives associated to certain algebraic Hecke characters
Shimura and Taniyama proved that if USD A USD is a potentially CM abelian variety over a number field USD F USD with CM by a field USD K USD linearly disjoint from F, then there is an algebraic Hecke character USD \lambda _A USD of USD FK USD such that USD L(A/F,s)=L(\lambda _A,s) USD. We consider a...
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| Format: | Journal article |
| Jezik: | English |
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American Mathematical Society
2018
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| _version_ | 1826258487403872256 |
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| author | Flapan, L Lang, J |
| author_facet | Flapan, L Lang, J |
| author_sort | Flapan, L |
| collection | OXFORD |
| description | Shimura and Taniyama proved that if USD A USD is a potentially CM abelian variety over a number field USD F USD with CM by a field USD K USD linearly disjoint from F, then there is an algebraic Hecke character USD \lambda _A USD of USD FK USD such that USD L(A/F,s)=L(\lambda _A,s) USD. We consider a certain converse to their result. Namely, let USD A USD be a potentially CM abelian variety appearing as a factor of the Jacobian of a curve of the form USD y^e=\gamma x^f+\delta USD. Fix positive integers USD a USD and USD n USD such that USD n/2 < a \leq n USD. Under mild conditions on USD e, f, \gamma , \delta USD, we construct a Chow motive USD M USD, defined over USD F=\mathbb{Q}(\gamma ,\delta )USD, such that USD L(M/F,s) USD and USD L(\lambda _A^a\overline {\lambda }_A^{n-a},s) USD have the same Euler factors outside finitely many primes. |
| first_indexed | 2024-03-06T18:34:48Z |
| format | Journal article |
| id | oxford-uuid:0ad49054-629b-4534-8ca2-ab14fcb5dbab |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:34:48Z |
| publishDate | 2018 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:0ad49054-629b-4534-8ca2-ab14fcb5dbab2022-03-26T09:26:20ZChow motives associated to certain algebraic Hecke charactersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0ad49054-629b-4534-8ca2-ab14fcb5dbabEnglishSymplectic ElementsAmerican Mathematical Society2018Flapan, LLang, JShimura and Taniyama proved that if USD A USD is a potentially CM abelian variety over a number field USD F USD with CM by a field USD K USD linearly disjoint from F, then there is an algebraic Hecke character USD \lambda _A USD of USD FK USD such that USD L(A/F,s)=L(\lambda _A,s) USD. We consider a certain converse to their result. Namely, let USD A USD be a potentially CM abelian variety appearing as a factor of the Jacobian of a curve of the form USD y^e=\gamma x^f+\delta USD. Fix positive integers USD a USD and USD n USD such that USD n/2 < a \leq n USD. Under mild conditions on USD e, f, \gamma , \delta USD, we construct a Chow motive USD M USD, defined over USD F=\mathbb{Q}(\gamma ,\delta )USD, such that USD L(M/F,s) USD and USD L(\lambda _A^a\overline {\lambda }_A^{n-a},s) USD have the same Euler factors outside finitely many primes. |
| spellingShingle | Flapan, L Lang, J Chow motives associated to certain algebraic Hecke characters |
| title | Chow motives associated to certain algebraic Hecke characters |
| title_full | Chow motives associated to certain algebraic Hecke characters |
| title_fullStr | Chow motives associated to certain algebraic Hecke characters |
| title_full_unstemmed | Chow motives associated to certain algebraic Hecke characters |
| title_short | Chow motives associated to certain algebraic Hecke characters |
| title_sort | chow motives associated to certain algebraic hecke characters |
| work_keys_str_mv | AT flapanl chowmotivesassociatedtocertainalgebraicheckecharacters AT langj chowmotivesassociatedtocertainalgebraicheckecharacters |