Namespace DeligneSerre 24 theorems
— 23 · OperatorAlgebra 1
directly in DeligneSerre 23
- Deligne–Serre: weight-one form with tame level exponents
DeligneSerre.exists_weightOne_cuspForm_tameConductor_of_qCoeff_eq_trace438 below · cited by 2 · depth 9 - Deligne–Serre: Euler factors and tame level exponents for weight one
DeligneSerre.eulerFactor_eq_and_tameLevel_of_weightOne_newform_qCoeff_eq_trace385 below · cited by 1 · depth 10 - Primes of finite torsion-free ℤ-algebras dominate characteristic-zero minimal primes
DeligneSerre.exists_minimalPrime_le0 below · cited by 4 · depth 10 - Characteristic zero for a quotient by an ideal meeting ℤ trivially
DeligneSerre.charZero_quotient0 below · cited by 3 · depth 11 - Deligne–Serre comparison of Euler products and conductors
DeligneSerre.eq_of_eulerProduct_completedLSeries_functionalEquation1 below · cited by 1 · depth 11 - Finite Euler products matched by a functional equation are trivial
DeligneSerre.eq_of_finite_eulerProduct_functionalEquation_of_norm_coeff_two_eq_one0 below · cited by 1 · depth 12 - Reduction of a common complex eigenvector modulo p
DeligneSerre.exists_modP_eigenvector_of_complex_eigenvector0 below · cited by 3 · depth 12 - Characteristic-zero eigenvector lifting a residual character
DeligneSerre.exists_charZero_eigenvector_of_residual_character2 below · cited by 1 · depth 13 - Deligne–Serre: Galois representation of a weight-one eigenform
DeligneSerre.exists_galoisRep_of_weightOne_qCoeff_hecke_eigen2,307 below · cited by 1 · depth 13 - Eigencharacter over ℤ̄ lifting a maximal ideal in the support
DeligneSerre.exists_eigencharacter_of_annihilator_le1 below · cited by 3 · depth 14 - Deligne–Serre: weight-one eigenvalues lie in an order, few exceptions
DeligneSerre.exists_finset_qCoeff_mem_of_upperDensity_le_of_weightOne_hecke_eigen850 below · cited by 1 · depth 14 - Deligne–Serre gluing: mod-ℓ family yields complex representation
DeligneSerre.exists_galoisRep_complex_trace_frobenius_eq_of_forall_residual32 below · cited by 1 · depth 14 - Deligne–Serre: uniform bound on mod-ℓ Galois images
DeligneSerre.exists_natCard_range_le_of_charpoly_frobenius_mem_of_upperDensity_le23 below · cited by 1 · depth 14 - Deligne–Serre: residual representation of a weight-one eigenform
DeligneSerre.exists_residual_galoisRep_charpoly_frobenius_eq_of_weightOne_hecke_eigen1,527 below · cited by 1 · depth 14 - Rankin's second-moment bound for weight-one Hecke eigenforms
DeligneSerre.exists_tsum_norm_qCoeff_sq_mul_rpow_le_log_of_weightOne_hecke_eigen794 below · cited by 2 · depth 14 - Deligne–Serre irreducibility criterion from a second-moment bound
DeligneSerre.isIrreducible_matrixRepresentation_of_tsum_norm_trace_sq_le_log_of_odd19 below · cited by 1 · depth 14 - Eigencharacter with prescribed minimal prime kernel
DeligneSerre.exists_eigenvector_of_mem_minimalPrimes_of_faithfulSMul0 below · cited by 3 · depth 15 - Residual Galois representation attached to a weight-two Hecke eigenform
DeligneSerre.exists_residual_galoisRep_charpoly_frobenius_eq_of_weightTwo_hecke_eigen1,515 below · cited by 1 · depth 15 - Deligne–Serre: conjugate eigensystems in weight one
DeligneSerre.exists_subalgebra_qCoeff_mem_forall_ringHom_exists_qCoeff_eq_of_weightOne_hecke_eigen70 below · cited by 1 · depth 15 - Weight-one mod-ℓ eigensystem realised in weight two
DeligneSerre.exists_weightTwo_hecke_eigen_reduction_eq_of_weightOne_hecke_eigen27 below · cited by 1 · depth 15 - Deligne–Serre lifting lemma for forms of type (w,ε)
DeligneSerre.exists_hecke_eigen_reduction_eq_of_qCoeff_hecke_congr14 below · cited by 1 · depth 16 - Deligne–Serre descent of χ₁⊕χ₂ to a finite field
DeligneSerre.exists_isSemisimpleRepresentation_charpoly_map_eq_of_add_mem_range_of_mul_mem_range0 below · cited by 1 · depth 17 - Deligne–Serre lifting: characteristic-zero factorisation of a character
DeligneSerre.exists_factorization_charZero_quotient2 below · cited by 1 · depth 18