Integral models of Shimura varieties with parahoric level structure

Kisin, M.; Pappas, G.

doi:10.1007/s10240-018-0100-0

Kisin, M. ; Pappas, G.

Publications Mathématiques de l'IHÉS, Tome 128 (2018), pp. 121-218.

Résumé

For a prime $p > 2$ , we construct integral models over $p$ for Shimura varieties with parahoric level structure, attached to Shimura data $(G, X)$ of abelian type, such that $G$ splits over a tamely ramified extension of $𝐐_{p}$ . The local structure of these integral models is related to certain “local models”, which are defined group theoretically. Under some additional assumptions, we show that these integral models satisfy a conjecture of Kottwitz which gives an explicit description for the trace of Frobenius action on their sheaf of nearby cycles.

Reçu le : 2015-11-27
Accepté le : 2018-03-28
Première publication : 2018-04-30
Publié le : 2018-11-09

DOI : 10.1007/s10240-018-0100-0

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     author = {Kisin, M. and Pappas, G.},
     title = {Integral models of {Shimura} varieties with parahoric level structure},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {121--218},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {128},
     year = {2018},
     doi = {10.1007/s10240-018-0100-0},
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Kisin, M.; Pappas, G. Integral models of Shimura varieties with parahoric level structure. Publications Mathématiques de l'IHÉS, Tome 128 (2018), pp. 121-218. doi : 10.1007/s10240-018-0100-0. http://archive.numdam.org/articles/10.1007/s10240-018-0100-0/

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