arXiv Open Access 2022

The connected components of affine Deligne--Lusztig varieties

Ian Gleason Dong Gyu Lim Yujie Xu

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Abstrak

We compute the connected components of arbitrary parahoric level affine Deligne-Lusztig varieties and local Shimura varieties, thus resolving a folklore conjecture in full generality (even for non-quasisplit groups). We achieve this by relating them to the connected components of infinite level moduli spaces of p-adic shtukas, where we use v-sheaf-theoretic techniques such as the specialization map of kimberlites. Along the way, we give a p-adic Hodge-theoretic characterization of HN-irreducibility. As applications, we obtain many results on the geometry of integral models of Shimura varieties of Hodge type at arbitrary stabilizer-parahoric levels. In particular, we deduce new CM lifting results on integral models of Shimura varieties for quasisplit groups at parahoric levels that arise as stabilizer Bruhat-Tits group schemes.

Topik & Kata Kunci

math.NT math.AG

Penulis (3)

Ian Gleason

Dong Gyu Lim

Yujie Xu

Format Sitasi

APA MLA BibTeX

Gleason, I., Lim, D.G., Xu, Y. (2022). The connected components of affine Deligne--Lusztig varieties. https://arxiv.org/abs/2208.07195

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓