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Article: The abelian part of a compatible system and ℓ-independence of the Tate conjecture
Title | The abelian part of a compatible system and ℓ-independence of the Tate conjecture |
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Authors | |
Issue Date | 2020 |
Citation | Manuscripta Mathematica, 2020, v. 161, n. 1-2, p. 223-246 How to Cite? |
Abstract | © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Let K be a number field and {Vℓ}ℓ a rational strictly compatible system of semisimple Galois representations of K arising from geometry. Let Gℓ and Vℓab be respectively the algebraic monodromy group and the maximal abelian subrepresentation of Vℓ for all ℓ. We prove that the system {Vℓab}ℓ is also a rational strictly compatible system under some group theoretic conditions, e.g., when Gℓ′ is connected and satisfies Hypothesis A for some prime ℓ′. As an application, we prove that the Tate conjecture for abelian variety X/K is independent of ℓ if the algebraic monodromy groups of the Galois representations of X satisfy the required conditions. |
Persistent Identifier | http://hdl.handle.net/10722/297373 |
ISSN | 2023 Impact Factor: 0.5 2023 SCImago Journal Rankings: 0.592 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Hui, Chun Yin | - |
dc.date.accessioned | 2021-03-15T07:33:38Z | - |
dc.date.available | 2021-03-15T07:33:38Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Manuscripta Mathematica, 2020, v. 161, n. 1-2, p. 223-246 | - |
dc.identifier.issn | 0025-2611 | - |
dc.identifier.uri | http://hdl.handle.net/10722/297373 | - |
dc.description.abstract | © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Let K be a number field and {Vℓ}ℓ a rational strictly compatible system of semisimple Galois representations of K arising from geometry. Let Gℓ and Vℓab be respectively the algebraic monodromy group and the maximal abelian subrepresentation of Vℓ for all ℓ. We prove that the system {Vℓab}ℓ is also a rational strictly compatible system under some group theoretic conditions, e.g., when Gℓ′ is connected and satisfies Hypothesis A for some prime ℓ′. As an application, we prove that the Tate conjecture for abelian variety X/K is independent of ℓ if the algebraic monodromy groups of the Galois representations of X satisfy the required conditions. | - |
dc.language | eng | - |
dc.relation.ispartof | Manuscripta Mathematica | - |
dc.title | The abelian part of a compatible system and ℓ-independence of the Tate conjecture | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00229-018-1068-2 | - |
dc.identifier.scopus | eid_2-s2.0-85077325989 | - |
dc.identifier.volume | 161 | - |
dc.identifier.issue | 1-2 | - |
dc.identifier.spage | 223 | - |
dc.identifier.epage | 246 | - |
dc.identifier.eissn | 1432-1785 | - |
dc.identifier.isi | WOS:000515760700012 | - |
dc.identifier.issnl | 0025-2611 | - |