Splitting and expliciting the de Rham complex of the Drinfeld space

2024/07/09 by Breuil, Christophe, Qian, Zicheng
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2407.06651

Abstract

Let p be a prime number, K a finite extension of ℚ_p and n an integer ≥ 2. We completely and explicitly describe the global sections Ω^\bullet of the de Rham complex of the Drinfeld space over K in dimension n-1 as a complex of (duals of) locally K-analytic representations of GL_n(K). Using this description, we construct an explicit section in the derived category of (duals of) finite length admissible locally K-analytic representations of GL_n(K) to the canonical morphism of complexes Ω^\bullet \twoheadrightarrow H^n-1(Ω^\bullet)[-(n-1)].

Related

• On the locally analytic Ext¹-conjecture in the GL₂(L) case
• Revêtements du demi-plan de Drinfeld et correspondance de Langlands p-adique
• On some partially de Rham Galois representations
• L'espace symétrique de Drinfeld et correspondance de Langlands locale I
• Equivariant Vector Bundles on the Drinfeld Upper Half Space over a Local Field of Positive Characteristic