On a conjecture of Kottwitz and Rapoport

Gashi, Qëndrim R.

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 6, pp. 1017-1038.

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.

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.

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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