Horizontal norm compatibility of cohomology classes for $\mathrm{GSp}_{6}$
| Autor: | Shah, Syed Waqar Ali |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We establish abstract horizontal norm relations involving the unramified Hecke-Frobenius polynomials that correspond under the Satake isomorhpism to the degree eight spinor $L$-factors of $ \mathrm{GSp}_{6} $. These relations apply to classes in the degree seven motivic cohomology of the Siegel modular sixfold obtained via Gysin pushforwards of Beilinson's Eisenstein symbol pulled back on one copy in a triple product of modular curves. The proof is based on a novel approach that circumvents the failure of the so-called multiplicity one hypothesis in our setting, which precludes the applicability of an existing technique. In a sequel, we combine our result with the previously established vertical norm relations for these classes to obtain new Euler systems for the eight dimensional Galois representations associated with certain non-endoscopic cohomological cuspidal automorphic representations of $ \mathrm{GSp}_{6} $. Comment: 52 pages. Comments welcome |
| Databáze: | arXiv |
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