Weil representation and Arithmetic Fundamental Lemma

2019/09/06 by Wei Zhang, Zhang, Wei · 4 citations
Mathematics · #11F67 #11G40 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1909.02697

openalex publication_date 2019/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By a global approach, we prove the arithmetic fundamental lemma conjecture for unitary groups in n variables over ℚ_p when p≥ n.

Citations

• Le lemme fondamental pour les algèbres de Lie
• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Arithmetic intersection theory
• A new proof of Jacquet-Rallis's fundamental lemma
• Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groups
• On Shimura varieties for unitary groups
• Kudla--Rapoport cycles and derivatives of local densities

Cited by

• The basic locus of regular ramified unitary Rapoport-Zink spaces at vertex-stabilizer level
• The basic locus of unitary splitting Rapoport-Zink spaces with vertex stabilizer level
• Gaussian test functions and Jacquet-Rallis transfer
• A Proof of the Biquadratic Linear AFL for GL(4)

Related

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• More Arithmetic Fundamental Lemma conjectures: the case of Bessel subgroups
• A geometric approach to the fundamental lemma for unitary groups
• On the Arithmetic Fundamental Lemma through Lie algebras
• Semi-Lie arithmetic fundamental lemma for the full spherical Hecke algebra