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Namespace PadicComplex 12 theorems

• Vanishing of ℂₚ(k)^{Gal(ℚ̄ₚ/K)} for k≠ 0 PadicComplex.eq_zero_of_forall_mem_fixingSubgroup_smul_eq_cyclotomicCharacter_zpow_mul 9 below · cited by 2 · depth 25
• Unit period for the determinant of an unramified representation PadicComplex.exists_ne_zero_forall_smul_eq_det_mul_of_forall_inertia_eq_one_of_ringOfIntegers 28 below · cited by 1 · depth 25
• Tate's vanishing: no nonzero χ^k-periods in ℂₚ PadicComplex.eq_zero_of_forall_smul_eq_cyclotomicCharacter_zpow_mul 7 below · cited by 2 · depth 26
• Vanishing of H¹(G_K,ℂₚ(χ^k)) for k≠ 0 PadicComplex.exists_eq_cyclotomicCharacter_zpow_mul_smul_sub_of_continuous_cocycle 19 below · cited by 1 · depth 26
• Galois descent of χ-equivariant functionals along a finite extension PadicComplex.exists_linearIndependent_forall_apply_eq_mul_smul_of_forall_mem_fixingSubgroup 1 below · cited by 1 · depth 26
• Tate: σ-μ is bijective on the completed tower PadicComplex.bijOn_towerClosure_smul_sub_mul_of_isTateTrace 0 below · cited by 1 · depth 27
• Vanishing of H¹_{cont}(Gal(ℚ̄ₚ/K_∞),ℂₚ) PadicComplex.exists_eq_smul_sub_of_continuous_cocycle_fixingSubgroup_sup_cyclotomicTower 12 below · cited by 1 · depth 27
• Bounded exponent for characters with a ℂₚ-period PadicComplex.exists_forall_pow_eq_one_of_isTateTrace_of_tmul_eq_mul 2 below · cited by 1 · depth 27
• Existence of Tate normalised traces on the cyclotomic tower PadicComplex.exists_isTateTrace_cyclotomicTower 3 below · cited by 2 · depth 27
• Ax–Sen–Tate: ℂₚ-invariants are the closure of K PadicComplex.forall_smul_eq_self_iff_mem_closure 1 below · cited by 4 · depth 27
• Tate: continuous ℂₚ-cocycles are coboundaries for almost étale F PadicComplex.exists_eq_smul_sub_of_continuous_cocycle_of_forall_exists_trace_eq 0 below · cited by 1 · depth 28
• Existence of Tate normalised traces on a p-adic tower PadicComplex.exists_isTateTrace_of_norm_sum_pow_apply_le 0 below · cited by 1 · depth 28