Namespace CartierDual 25 theorems
- The Cartier dual of R[M] is étale for finite M
CartierDual.algebraEtale_addMonoidAlgebra0 below · cited by 5 · depth 13 - Cartier duality commutes with base change: finite free case
CartierDual.dualBaseChangeLin_bijective_integral0 below · cited by 8 · depth 14 - Cartier dual of R[Γ] is Map(Γ,R)
CartierDual.exists_algEquiv_monoidAlgebra_pi0 below · cited by 4 · depth 14 - Cartier dual corepresents group-like elements
CartierDual.exists_algHomEquiv_groupLike0 below · cited by 6 · depth 14 - Cartier biduality for finite free cocommutative bialgebras
CartierDual.exists_bialgEquiv_bidual0 below · cited by 13 · depth 14 - Evaluation at convolution points identifies A with R[Γ]^∨
CartierDual.exists_bialgEquiv_monoidAlgebra_of_points0 below · cited by 4 · depth 14 - Cartier duality commutes with base change to a field
CartierDual.dualBaseChangeLin_bijective0 below · cited by 4 · depth 16 - Annihilator of I_S as a Hopf subalgebra of the Cartier dual
CartierDual.exists_subalgebra_eq_annihilator_vanishingIdealOfPoints0 below · cited by 1 · depth 16 - Galois-equivariant Cartier duality over ℚ̄ₚ
CartierDual.exists_equiv_algHom_padicAlgCl_monoidHom_units11 below · cited by 5 · depth 17 - Cartier duality commutes with base change
CartierDual.nonempty_ringEquiv_baseChange0 below · cited by 4 · depth 17 - Orthogonal idempotents in the Cartier dual give a coalgebra map
CartierDual.exists_coalgHom_addMonoidAlgebra_eq_sum_single_of_isIdempotentElem0 below · cited by 1 · depth 18 - Coalgebra maps B → S[M] give orthogonal idempotents in the Cartier dual
CartierDual.exists_isIdempotentElem_eq_sum_single_of_coalgHom_addMonoidAlgebra0 below · cited by 2 · depth 18 - Reduction of the Cartier dual modulo 𝔪
CartierDual.exists_ringHom_apply_eq_dualBaseChangeLin_tmul_of_isLocalRing1 below · cited by 1 · depth 18 - Locality of H and of H^D descends to the fibre over k₀
CartierDual.isLocalRing_baseChange_and_isLocalRing_cartierDual_baseChange4 below · cited by 5 · depth 18 - Local Cartier dual descends to quotient Hopf algebras
CartierDual.isLocalRing_cartierDual_of_bialgHom_surjective0 below · cited by 2 · depth 18 - Cartier duality commutes with base change
CartierDual.exists_bialgEquiv_baseChange_forall_pairing_symm_tmul0 below · cited by 6 · depth 19 - Cartier duality on L-points, Galois-equivariantly
CartierDual.exists_equiv_algHom_monoidHom_units_of_isAlgClosed_of_charZero11 below · cited by 1 · depth 19 - Local–local is inherited by bialgebra quotients
CartierDual.isLocalRing_and_isLocalRing_cartierDual_of_bialgHom_surjective_univ0 below · cited by 1 · depth 20 - Basis independence, naturality and bimultiplicativity of the Cartier pairing
CartierDual.basisPairing_eq_and_map_convMul_and_comp_and_transpose0 below · cited by 6 · depth 25 - Exactness of Cartier duality for a Hopf quotient
CartierDual.forall_hopfKer_apply_eq_zero_iff_mem_map_ker_counit5 below · cited by 2 · depth 25 - p-th convolution power of an ε-derivation
CartierDual.pow_char_apply_mul_of_apply_mul0 below · cited by 1 · depth 25 - Cartier dual characters determined on the connected factor
CartierDual.algHom_comp_map_eq_of_comp_eq_comp_of_bijective_tensorProduct_of_isReduced_of_nsmulAlgHom_pow_eq_zmodp3 below · cited by 1 · depth 28 - Base change commutes with the Cartier transpose of an endomorphism
CartierDual.dualBaseChangeLin_lTensor_map_eq_map_baseChange_dualBaseChangeLin0 below · cited by 1 · depth 28 - Frobenius–Verschiebung identity paired on the Cartier dual
CartierDual.pow_apply_pow_eq_apply_nsmulAlgHom_pow0 below · cited by 3 · depth 28 - Cartier-dual points of a reduced p^N-killed Hopf algebra
CartierDual.algHom_apply_eq_algebraMap_apply_one_of_isReduced_of_nsmulAlgHom_pow_eq_zmodp2 below · cited by 1 · depth 29