An alternative description of the Drinfeld p-adic half-plane
Annales de l'Institut Fourier, Volume 64 (2014) no. 3, p. 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 : https://doi.org/10.5802/aif.2878
Classification:  11G18,  14G35,  11G15
Keywords: Drinfeld p-adic half-plane, Bruhat-Tits tree
@article{AIF_2014__64_3_1203_0,
     author = {Kudla, Stephen and Rapoport, Michael},
     title = {An alternative description of the Drinfeld $p$-adic half-plane},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {3},
     year = {2014},
     pages = {1203-1228},
     doi = {10.5802/aif.2878},
     mrnumber = {3330168},
     zbl = {06387305},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_3_1203_0}
}
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. http://www.numdam.org/item/AIF_2014__64_3_1203_0/

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