We show that the Deligne formal model of the Drinfeld -adic half-plane relative to a local field represents a moduli problem of polarized -modules with an action of the ring of integers in a quadratic extension of . The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of and for a two-dimensional split hermitian space for .
On montre que le modèle formel dû à Deligne du demi-plan -adique de Drinfeld relatif à un corps -adique représente un problème de modules de -modules munis d’une action de l’anneau des entiers dans une extension quadratique de . La démonstration repose sur une comparaison entre ce problème de modules et celui de Drinfeld des -modules formels spéciaux. Cet isomorphisme est une manifestation de l’isomorphisme exceptionel entre et , où est un espace hermitien déployé de dimension sur .
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
@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}, pages = {1203--1228}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {3}, year = {2014}, doi = {10.5802/aif.2878}, mrnumber = {3330168}, zbl = {06387305}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2878/} }
TY - JOUR AU - Kudla, Stephen AU - Rapoport, Michael TI - An alternative description of the Drinfeld $p$-adic half-plane JO - Annales de l'Institut Fourier PY - 2014 SP - 1203 EP - 1228 VL - 64 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2878/ DO - 10.5802/aif.2878 LA - en ID - AIF_2014__64_3_1203_0 ER -
%0 Journal Article %A Kudla, Stephen %A Rapoport, Michael %T An alternative description of the Drinfeld $p$-adic half-plane %J Annales de l'Institut Fourier %D 2014 %P 1203-1228 %V 64 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2878/ %R 10.5802/aif.2878 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2878/
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