On a conjecture of Kottwitz and Rapoport
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 43 (2010) no. 6, pp. 1017-1038.

We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur's Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.

On démontre une conjecture de Kottwitz et Rapoport sur une réciproque à l'inégalité de Mazur pour tout groupe (connexe) réductif, déployé ou quasi-déployé non-ramifié. Nos résultats sont liés à la non-vacuité de certaines variétés de Deligne-Lusztig affines.

DOI: 10.24033/asens.2138
Classification: 14L15, 14M15, 20G25
Keywords: Newton polygon, isocrystal, affine Deligne-Lusztig variety
Mot clés : polygone de Newton, isocristal, variétés de Deligne-Lusztig affines
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     title = {On a conjecture of {Kottwitz} and {Rapoport}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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     volume = {Ser. 4, 43},
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Gashi, Qëndrim R. On a conjecture of Kottwitz and Rapoport. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 43 (2010) no. 6, pp. 1017-1038. doi : 10.24033/asens.2138. http://www.numdam.org/articles/10.24033/asens.2138/

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