Faltings’ Local-Global Principle for the Minimaxness of Local Cohomology Modules Defined by a System of Ideals

Key Points

• This research aims to establish local-global principles for the minimaxness of generalized local cohomology modules associated with a system of ideals.
• Analyzed local cohomology modules H_φ^i (M, N) derived from an ideal system in a Noetherian ring.
• Proved finite and minimax properties of these modules under specific conditions.
• Demonstrated new local-global principles for the finiteness of generalized local cohomology modules.
• Established criteria for minimaxness in certain local cohomology contexts.