Galois representations for even general special orthogonal groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866912124448538624 |
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| author | Kret, Arno Shin, Sug Woo |
| author_facet | Kret, Arno Shin, Sug Woo |
| contents | We prove the existence of $\mathrm{GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\mathrm{GSO}_{2n}$ under the local hypotheses that there is a Steinberg component and that the archimedean parameters are regular for the standard representation. This is based on the cohomology of Shimura varieties of abelian type, of type $D^{\mathbb{H}}$, arising from forms of $\mathrm{GSO}_{2n}$. As an application, under similar hypotheses, we compute automorphic multiplicities, prove meromorphic continuation of (half) spin $L$-functions, and improve on the construction of $\mathrm{SO}_{2n}$-valued Galois representations by removing the outer automorphism ambiguity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_08408 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Galois representations for even general special orthogonal groups Kret, Arno Shin, Sug Woo Number Theory Representation Theory We prove the existence of $\mathrm{GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\mathrm{GSO}_{2n}$ under the local hypotheses that there is a Steinberg component and that the archimedean parameters are regular for the standard representation. This is based on the cohomology of Shimura varieties of abelian type, of type $D^{\mathbb{H}}$, arising from forms of $\mathrm{GSO}_{2n}$. As an application, under similar hypotheses, we compute automorphic multiplicities, prove meromorphic continuation of (half) spin $L$-functions, and improve on the construction of $\mathrm{SO}_{2n}$-valued Galois representations by removing the outer automorphism ambiguity. |
| title | Galois representations for even general special orthogonal groups |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2010.08408 |