Cohomologie mod p des fibrés en droites équivariants sur le demi-plan de Drinfeld

2023/06/15 by Damien Junger, Junger, Damien
Mathematics · #11F12 #11F33 #11F80 #11F85 #11G09 #11G18 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.09007

openalex publication_date 2023/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a classification of all equivariant line of bundles on the semi-stable model ℍ of the Drinfeld upper half plane ℍ on ℚ_p for a certain subgroup [G]₂ of \rm GL₂(ℚ_p) of index 2. Then we study the cohomology groups of these line bundles that we restrict on the special fiber ℍ and this process provides a whole family of mod p representations. In particular, we exhibit a class of [G]₂-equivariant line bundles on ℍ (the so-called positives of weight -1) and show that they are in one-to-one correspondence with the irreducible supersingular representations of [G]₂ (a notion we define) by taking the contragredient of the global sections.

Related

• Classification of Equivariant Line Bundles on the Drinfeld Upper Half Plane
• Equivariant line bundles with connection on the p-adic upper half plane
• Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces
• Equivariant Vector Bundles on the Drinfeld Upper Half Space over a Local Field of Positive Characteristic
• Equivariant vector bundles on Drinfeld's upper half space