2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215098Let $R$ be a polynomial ring in finitely many variables over the integers, and fix an ideal $I$ of $R$. We prove that for all but finitely prime integers $p$, the Bockstein homomorphisms on local cohomology, $H^k_I(R/pR)\to H^{k+1}_I(R/pR)$, are zero. This provides strong evidence for Lyubeznik's conjecture which states that the modules $H^k_I(R)$ have a finite number of associated prime ideals.Commutative Algebra13D45; 13F20, 13F55.text