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Automorphy and irreducibility of some l-adic representations
| Content Provider | Scilit |
|---|---|
| Author | Patrikis, Stefan Taylor, Richard |
| Copyright Year | 2014 |
| Description | Journal: Compositio Mathematica In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of $l$ -adic representations is potentially automorphic. The innovation is that we make no irreducibility assumption, but we make a purity assumption instead. For compatible systems coming from geometry, purity is often easier to check than irreducibility. We use Katz’s theory of rigid local systems to construct many examples of motives to which our theorem applies. We also show that if $F$ is a CM or totally real field and if ${\it\pi}$ is a polarizable, regular algebraic, cuspidal automorphic representation of $\text{GL}_{n}(\mathbb{A}_{F})$ , then for a positive Dirichlet density set of rational primes $l$ , the $l$ -adic representations $r_{l,\imath }({\it\pi})$ associated to ${\it\pi}$ are irreducible. |
| Ending Page | 229 |
| Starting Page | 207 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x14007519 |
| Journal | Compositio Mathematica |
| Issue Number | 2 |
| Volume Number | 151 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2014-10-24 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Mathematical Physics Adic Representations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
