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Let $π$ be a regular, algebraic, essentially self-dual cuspidal automorphic representation of ${GL}_{n} (𝔸_{F})$ , where $F$ is a totally real field and $n$ is at most $5$ . We show that for all primes $l$ , the $l$ -adic Galois representations associated to $π$ are irreducible, and for all but finitely many primes $l$ , the mod $l$ Galois representations associated to $π$ are also irreducible. We also show that the Lie algebras of the Zariski closures of the $l$ -adic representations are independent of $l$ .

Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes

Robert Harron, Antonio Lei (2014)

Journal de Théorie des Nombres de Bordeaux

Let $f$ be a cuspidal newform with complex multiplication (CM) and let $p$ be an odd prime at which $f$ is non-ordinary. We construct admissible $p$ -adic $L$ -functions for the symmetric powers of $f$ , thus verifying conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus $p$ -adic $L$ -functions and prove an analogue of Pollack’s decomposition of the admissible $p$ -adic $L$ -functions....

Displaying 1 – 6 of 6

Inductivity of the global root number

Infinitely ramified Galois representations.

Integral G -structures of Wach modules. ( G -structures entières et modules de Wach.)

Invariant L et série spéciale p-adique

Irreducibility of automorphic Galois representations of G L ( n ) , n at most 5

Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes

Currently displaying 1 – 6 of 6

Integral $G$ -structures of Wach modules. ( $G$ -structures entières et modules de Wach.)

Invariant $L$ et série spéciale p-adique

Irreducibility of automorphic Galois representations of $G L (n)$ , $n$ at most $5$