Ordinary local representations and \Ext groups

2022/10/05 by Debargha Banerjee, Banerjee, Debargha, Das, Srijan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2210.02238

Abstract

We can associate an admissible unitary representation Π(ρ_p) of \GL₂(\Q_p) with every local Galois representation ρ_p by the p-adic local Langlands correspondence. If ρ_p is ordinary, we prove local and global vanishing results for \Ext functors with respect to these representations.

Related

• The p-adic local Langlands correspondence for GL₂(Q_p)
• Strong local-global compatibility in the p-adic Langlands program for U(2)
• Locally analytic vectors of unitary principal series of GL₂(Qp)
• Moduli stacks of Galois representations and the p-adic local Langlands correspondence for GL₂(ℚ_p)
• The Local Langlands correspondence for \GL_n over p-adic fields