CHAO MA

Augmentation-Ideal Realization of Special Nottingham Congruence Series and Cartier Indecomposables

Let k = F_p with p >= 5, let A = k[[x_1,...,x_n]] with n >= 3, and let m be its maximal ideal. Let G be the group of volume-preserving formal automorphisms of A tangent to the identity, let G_s consist of those g in G such that g(x_i) - x_i lies in m^s for every i, and let T_N =...

The First Frattini–Commutator Layer of Jacobian-One Formal Automorphisms

Let k = F_p with p >= 5, let V = k^n with n >= 3, and let G_1 be the tangent-to-the-identity Jacobian-one formal automorphism group, with congruence quotients T_N and Frattini subgroups Phi_N. We determine the first Frattini-commutator layer J_N = [T_N,Phi_N] / ([T_N,[T_N,Phi_N]]...

Cartier Relation Symbols and Frattini Transgression in Special Nottingham Groups

Let k = F_p, let V = k^n with n >= 3, and let T_N be a finite congruence quotient of the tangent-to-identity Jacobian-one automorphism group of k[[x_1,...,x_n]]. Put d_r = (p - 1)(n - 1) + pr, and let L_s be the coefficient-degree-s divergence-free polynomial vector fields. Carti...

The Critical Cartier Diagonal in the Lower p-Central Series of Jacobian-One Formal Automorphisms

Let k = F_p with p ≥ 5, let V = k^n with n ≥ 3, and let T(N) be a finite congruence quotient of the tangent-to-the-identity Jacobian-one formal automorphism group in n variables. Write P(1) = T(N), P(i + 1) = P(i)^p[P(i), T(N)], and d(r) = (p − 1)(n − 1) + pr. For every r ≥ 2 and...

Cartier Relation Symbols and Frattini Transgression in Special Nottingham Groups

Let k = F_p, let V = k^n with n >= 3, and let T_N be a finite congruence quotient of the tangent-to-identity Jacobian-one automorphism group of k[[x_1,...,x_n]]. Put d_r = (p - 1)(n - 1) + pr, and let L_s be the coefficient-degree-s divergence-free polynomial vector fields. Carti...

The Critical Cartier Diagonal in the Lower p-Central Series of Jacobian-One Formal Automorphisms

Let k = F_p with p ≥ 5, let V = k^n with n ≥ 3, and let T(N) be a finite congruence quotient of the tangent-to-the-identity Jacobian-one formal automorphism group in n variables. Write P(1) = T(N), P(i + 1) = P(i)^p[P(i), T(N)], and d(r) = (p − 1)(n − 1) + pr. For every r ≥ 2 and...

The First Frattini–Commutator Layer of Jacobian-One Formal Automorphisms

Let k = F_p with p >= 5, let V = k^n with n >= 3, and let G_1 be the tangent-to-the-identity Jacobian-one formal automorphism group, with congruence quotients T_N and Frattini subgroups Phi_N. We determine the first Frattini-commutator layer J_N = [T_N,Phi_N] / ([T_N,[T_N,Phi_N]]...