Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families
Let f and g be two cuspidal modular forms and let F be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space W . Using ideas of Pottharst, under certain hypotheses on f and g, we construct a coherent sheaf over V×W that interpolates the Bloch–Kato Selmer group...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Canadian Mathematical Society
2020
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| _version_ | 1826281890907160576 |
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| author | Graham, A Gulotta, DR Xu, Y |
| author_facet | Graham, A Gulotta, DR Xu, Y |
| author_sort | Graham, A |
| collection | OXFORD |
| description | Let f and g be two cuspidal modular forms and let F be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space W . Using ideas of Pottharst, under certain hypotheses on f and g, we construct a coherent sheaf over V×W that interpolates the Bloch–Kato Selmer group of the Rankin–Selberg convolution of two modular forms in the critical range (i.e, the range where the p-adic L-function 𝐿𝑝 interpolates critical values of the global L-function). We show that the support of this sheaf is contained in the vanishing locus of 𝐿𝑝 . |
| first_indexed | 2024-03-07T00:35:37Z |
| format | Journal article |
| id | oxford-uuid:814a9f3b-231b-4799-97f2-b8f12c0b3316 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:35:37Z |
| publishDate | 2020 |
| publisher | Canadian Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:814a9f3b-231b-4799-97f2-b8f12c0b33162022-03-26T21:29:26ZBounding Selmer groups for the Rankin–Selberg convolution of Coleman familiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:814a9f3b-231b-4799-97f2-b8f12c0b3316EnglishSymplectic ElementsCanadian Mathematical Society2020Graham, AGulotta, DRXu, YLet f and g be two cuspidal modular forms and let F be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space W . Using ideas of Pottharst, under certain hypotheses on f and g, we construct a coherent sheaf over V×W that interpolates the Bloch–Kato Selmer group of the Rankin–Selberg convolution of two modular forms in the critical range (i.e, the range where the p-adic L-function 𝐿𝑝 interpolates critical values of the global L-function). We show that the support of this sheaf is contained in the vanishing locus of 𝐿𝑝 . |
| spellingShingle | Graham, A Gulotta, DR Xu, Y Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families |
| title | Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families |
| title_full | Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families |
| title_fullStr | Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families |
| title_full_unstemmed | Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families |
| title_short | Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families |
| title_sort | bounding selmer groups for the rankin selberg convolution of coleman families |
| work_keys_str_mv | AT grahama boundingselmergroupsfortherankinselbergconvolutionofcolemanfamilies AT gulottadr boundingselmergroupsfortherankinselbergconvolutionofcolemanfamilies AT xuy boundingselmergroupsfortherankinselbergconvolutionofcolemanfamilies |