Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive in...
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| Language: | English |
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Springer-Verlag
2017
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| Online Access: | http://hdl.handle.net/1721.1/109571 |
| _version_ | 1826209608985739264 |
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| author | Arias-de-Reyna, Sara Dieulefait, Luis V. Shin, Sug Woo Wiese, Gabor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Arias-de-Reyna, Sara Dieulefait, Luis V. Shin, Sug Woo Wiese, Gabor |
| author_sort | Arias-de-Reyna, Sara |
| collection | MIT |
| description | This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive integer n and any positive integer d, PSp[subscript n](F[subscript ℓ[superscript d]]) or PGSp[subscript n](F[subscript ℓ[superscript d]]) occurs as a Galois group over the rational numbers for a positive density set of primes ℓ. The result depends on some work of Arthur’s, which is conditional, but expected to become unconditional soon. The result is obtained by showing the existence of a regular, algebraic, self-dual, cuspidal automorphic representation of GL[subscript n](A[subscript Q]) with local types chosen so as to obtain a compatible system of Galois representations to which the results from Part II of this series apply. |
| first_indexed | 2024-09-23T14:25:10Z |
| format | Article |
| id | mit-1721.1/109571 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:25:10Z |
| publishDate | 2017 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/1095712022-10-01T21:15:02Z Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties Arias-de-Reyna, Sara Dieulefait, Luis V. Shin, Sug Woo Wiese, Gabor Massachusetts Institute of Technology. Department of Mathematics Shin, Sug Woo This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive integer n and any positive integer d, PSp[subscript n](F[subscript ℓ[superscript d]]) or PGSp[subscript n](F[subscript ℓ[superscript d]]) occurs as a Galois group over the rational numbers for a positive density set of primes ℓ. The result depends on some work of Arthur’s, which is conditional, but expected to become unconditional soon. The result is obtained by showing the existence of a regular, algebraic, self-dual, cuspidal automorphic representation of GL[subscript n](A[subscript Q]) with local types chosen so as to obtain a compatible system of Galois representations to which the results from Part II of this series apply. National Science Foundation (U.S.) (DMS-1162250) Alfred P. Sloan Foundation. Fellowship 2017-06-02T20:54:04Z 2017-06-02T20:54:04Z 2014-09 2014-07 2016-05-23T12:09:03Z Article http://purl.org/eprint/type/JournalArticle 0025-5831 1432-1807 http://hdl.handle.net/1721.1/109571 Arias-de-Reyna, Sara, Luis V. Dieulefait, Sug Woo Shin, and Gabor Wiese. “Compatible Systems of Symplectic Galois Representations and the Inverse Galois Problem III. Automorphic Construction of Compatible Systems with Suitable Local Properties.” Math. Ann. 361, no. 3–4 (September 7, 2014): 909–925. © 2104 Springer-Verlag en http://dx.doi.org/10.1007/s00208-014-1091-x Mathematische Annalen Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag Berlin Heidelberg application/pdf Springer-Verlag Springer Berlin Heidelberg |
| spellingShingle | Arias-de-Reyna, Sara Dieulefait, Luis V. Shin, Sug Woo Wiese, Gabor Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties |
| title | Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties |
| title_full | Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties |
| title_fullStr | Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties |
| title_full_unstemmed | Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties |
| title_short | Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties |
| title_sort | compatible systems of symplectic galois representations and the inverse galois problem iii automorphic construction of compatible systems with suitable local properties |
| url | http://hdl.handle.net/1721.1/109571 |
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