An alternative description of the Drinfeld p-adic half-plane
Annales de l'Institut Fourier, Volume 64 (2014) no. 3, pp. 1203-1228.

We show that the Deligne formal model of the Drinfeld p-adic half-plane relative to a local field F represents a moduli problem of polarized O F -modules with an action of the ring of integers in a quadratic extension E of F. The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of SL 2 (F) and SU (C)(F) for a two-dimensional split hermitian space C for E/F.

On montre que le modèle formel dû à Deligne du demi-plan p-adique de Drinfeld relatif à un corps p-adique F représente un problème de modules de O F -modules munis d’une action de l’anneau des entiers dans une extension quadratique E de F. La démonstration repose sur une comparaison entre ce problème de modules et celui de Drinfeld des O D -modules formels spéciaux. Cet isomorphisme est une manifestation de l’isomorphisme exceptionel entre SL 2 (F) et SU(C)(F), où C est un espace hermitien déployé de dimension 2 sur E.

DOI: 10.5802/aif.2878
Classification: 11G18, 14G35, 11G15
Keywords: Drinfeld $p$-adic half-plane, Bruhat-Tits tree
Mot clés : demi-plan de Drinfeld $p$-adique, arbre de Bruhat-Tits

Kudla, Stephen 1; Rapoport, Michael 2

1 University of Toronto Department of Mathematics 40 St. George St., BA6290 Toronto, Ontario, M5S 2E4 (Canada)
2 Mathematisches Institut der Universität Bonn Endenicher Allee 60 53115 Bonn (Allemagne)
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Kudla, Stephen; Rapoport, Michael. An alternative description of the Drinfeld $p$-adic half-plane. Annales de l'Institut Fourier, Volume 64 (2014) no. 3, pp. 1203-1228. doi : 10.5802/aif.2878. https://aif.centre-mersenne.org/articles/10.5802/aif.2878/

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