Mathematics > Number Theory
[Submitted on 29 Jun 2024
(v1)
, last revised 4 Jul 2024 (this version, v2)]
Title: A Rank-Two Case of Local-Global Compatibility for $l = p$
Title: 秩为二的局部-整体相容性$l = p$案例
Abstract: We prove the classical $l = p$ local-global compatibility conjecture for certain regular algebraic cuspidal automorphic representations of weight 0 for GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the automorphic side comes from a twist of Steinberg at $v | l$, then the Galois side has nontrivial monodromy at $v$. Based on this observation, we will give a definition of the Fontaine-Mazur $\mathcal{L}$-invariants attached to certain automorphic representations.
Submission history
From: Yuji Yang [view email][v1] Sat, 29 Jun 2024 02:52:13 UTC (18 KB)
[v2] Thu, 4 Jul 2024 15:27:22 UTC (18 KB)
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