Iwasawa theory of automorphic representations of GL_2n at non-ordinary primes

2020/10/01 by Antonio Lei, Lei, Antonio, Jishnu Ray +1
Mathematics · #11F67 #11F80 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary: 11R23 #Representation Theory (math.RT) #Secondary: 11F70

paper · pdf · doi:10.48550/arxiv.2010.00715

openalex publication_date 2020/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Π be a cuspidal automorphic representation of GL_2n(\mathbbA_Q) and let p be an odd prime at which Π is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded p-adic L-functions interpolating complex L-values of Π in the non-ordinary case. Under certain assumptions, we construct two bounded p-adic L-functions for Π, thus extending an earlier work of Rockwood by relaxing the Pollack condition. Using Langlands local-global compatibility, we define signed Selmer groups over the p-adic cyclotomic extension of ℚ attached to the p-adic Galois representation of Π and formulate Iwasawa main conjectures in the spirit of Kobayashi's plus and minus main conjectures for p-supersingular elliptic curves.

Citations

• On the Asymptotic Growth ofBloch-Kato-Shafarevich-Tate Groups ofModular Forms Over CyclotomicExtensions
• On the Bloch-Kato conjecture for GSp(4)

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