First explicit reciprocity law for unitary Friedberg—Jacquet periods
In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many breakthroughs on constr...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/155381 https://orcid.org/0000-0003-3742-0992 |
| _version_ | 1811072496464560128 |
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| author | Corato Zanarella, Murilo |
| author2 | Zhang, Wei |
| author_facet | Zhang, Wei Corato Zanarella, Murilo |
| author_sort | Corato Zanarella, Murilo |
| collection | MIT |
| description | In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many breakthroughs on constructing such systems for other Galois representations, including settings such as twisted and cubic triple product, symmetric cube, and Rankin--Selberg, with applications to the Bloch--Kato conjecture and to Iwasawa theory.
This thesis studies the case of Galois representations attached to automorphic representations on a totally definite unitary group U(2r) over a CM field which are distinguished by the subgroup U(r) x U(r). We prove a new ``first explicit reciprocity law'' in this setting, which has applications to the rank 0 case of the corresponding Bloch--Kato conjecture. |
| first_indexed | 2024-09-23T09:06:53Z |
| format | Thesis |
| id | mit-1721.1/155381 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:06:53Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1553812024-06-28T03:55:24Z First explicit reciprocity law for unitary Friedberg—Jacquet periods Corato Zanarella, Murilo Zhang, Wei Massachusetts Institute of Technology. Department of Mathematics In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many breakthroughs on constructing such systems for other Galois representations, including settings such as twisted and cubic triple product, symmetric cube, and Rankin--Selberg, with applications to the Bloch--Kato conjecture and to Iwasawa theory. This thesis studies the case of Galois representations attached to automorphic representations on a totally definite unitary group U(2r) over a CM field which are distinguished by the subgroup U(r) x U(r). We prove a new ``first explicit reciprocity law'' in this setting, which has applications to the rank 0 case of the corresponding Bloch--Kato conjecture. Ph.D. 2024-06-27T19:49:15Z 2024-06-27T19:49:15Z 2024-05 2024-05-15T16:20:11.372Z Thesis https://hdl.handle.net/1721.1/155381 https://orcid.org/0000-0003-3742-0992 In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Corato Zanarella, Murilo First explicit reciprocity law for unitary Friedberg—Jacquet periods |
| title | First explicit reciprocity law for unitary Friedberg—Jacquet periods |
| title_full | First explicit reciprocity law for unitary Friedberg—Jacquet periods |
| title_fullStr | First explicit reciprocity law for unitary Friedberg—Jacquet periods |
| title_full_unstemmed | First explicit reciprocity law for unitary Friedberg—Jacquet periods |
| title_short | First explicit reciprocity law for unitary Friedberg—Jacquet periods |
| title_sort | first explicit reciprocity law for unitary friedberg jacquet periods |
| url | https://hdl.handle.net/1721.1/155381 https://orcid.org/0000-0003-3742-0992 |
| work_keys_str_mv | AT coratozanarellamurilo firstexplicitreciprocitylawforunitaryfriedbergjacquetperiods |