Elementary Abelian P-Kernels Have Augmentation-Ideal Norm Homology
Epistemic-graph event: 1364.
For a rank-k kernel in (C_p)^n over F_p, the norm is the top monomial
product epsilon_i^(p-1).
Its square-zero homology is
(I_B/Soc(A_B)) tensor A_(B^c),
with total dimension p^(n-k)(p^k-2) and collapsed-kernel Loewy length
k(p-1)-1. Its Hilbert series is obtained from the truncated-polynomial
series by deleting the unit and top socle terms in the collapsed factor.
The only zero case is one C2 direction in characteristic two. A one-bit
C3 kernel already leaves one residual class per fiber. The five-site
mod-two results are the specialization p=2,n=5.
This remains modular deck algebra, not a physical relative-chain theorem.
Research note:
research/grothendieck/elementary-abelian-p-norm-homology.md.