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Global \(\textbf{B}(G)\) with adelic coefficients and transfer factors at non-regular elements

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Abstract

The goal of this paper is extend Kottwitz’s theory of B(G) for global fields. In particular, we show how to extend the definition of “B(G) with adelic coefficients” from tori to all connected reductive groups. As an application, we give an explicit construction of certain transfer factors for non-regular semisimple elements of non-quasisplit groups. This generalizes some results of Kaletha and Taibi. These formulas are used in the stabilization of the cohomology of Shimura and Igusa varieties.

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Acknowledgements

I would like to thank Tasho Kaletha for many helpful discussions and suggestions. I am also grateful for conversations with Sug Woo Shin and Alex Youcis which influenced my thoughts on the contents of this paper. This research was partially supported by NSF RTG Grant DMS-1840234.

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  1. University of Michigan, 530 Church St, Ann Arbor, MI, 48109, USA

    Alexander Bertoloni Meli

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Meli, A.B. Global \(\textbf{B}(G)\) with adelic coefficients and transfer factors at non-regular elements. Math. Z. 306, 74 (2024). https://doi.org/10.1007/s00209-024-03454-3

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