Conjugates of Rational Equivariant Holomorphic Maps of Symmetric Domains
Equivariant holomorphic maps, Hermitian symmetric domains, Kuga fiber varieties, Locally symmetric spaces
Monatshefte fur Mathematik
Let τ : script D sign → script D sign′ be an equivariant holomorphic map of symmetric domains associated to a homomorphism ρ : double-struct G sign → double-struct G sign′ of semisimple algebraic groups defined over ℚ. If Γ ⊂ double-struct G sign (ℚ) and Γ′ ⊂ double-struct G sign′(ℚ) are torsion-free arithmetic subgroups with ρ (Γ)⊂ Γ′, the map τ induces a morphism φ: Γ/script D sign → Γ′/script D sign′ of arithmetic varieties and the rationality of τ is defined by using symmetries on script D sign and script D sign′ as well as the commensurability groups of Γ and Γ′. An element σ ∈ Aut(ℂ) determines a conjugate equivariant holomorphic map τσ : script D sign;σ → script D sign′σ of τ which induces the conjugate morphism φσ : (Γ/script D sign)σ → (Γ′/script D sign′)σ of φ. We prove that τσ is rational if τ is rational.
Original Publication Date
DOI of published version
Lee, Min Ho, "Conjugates of Rational Equivariant Holomorphic Maps of Symmetric Domains" (2004). Faculty Publications. 3183.