Algebra & Number Theory

The Tannakian formalism and the Langlands conjectures

David Kazhdan, Michael Larsen, and Yakov Varshavsky

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Let H be a connected reductive group over an algebraically closed field of characteristic zero, and let Γ be an abstract group. In this note, we show that every homomorphism of Grothendieck semirings ϕ:K0+[H]K0+[Γ], which maps irreducible representations to irreducible, comes from a group homomorphism ρ:ΓH(K). We also connect this result with the Langlands conjectures.

Article information

Algebra Number Theory, Volume 8, Number 1 (2014), 243-256.

Received: 2 September 2012
Revised: 20 August 2013
Accepted: 19 September 2013
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 11R39: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
Secondary: 11F80: Galois representations 17B10: Representations, algebraic theory (weights) 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]

Tannaka duality Langlands conjectures


Kazhdan, David; Larsen, Michael; Varshavsky, Yakov. The Tannakian formalism and the Langlands conjectures. Algebra Number Theory 8 (2014), no. 1, 243--256. doi:10.2140/ant.2014.8.243.

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