Cohomological Mackey functors in number theory

We prove relations between the evaluations of cohomological Mackey functors over complete discrete valuation rings or fields and apply this to Mackey functors that arise naturally in number theory. This provides relations between λ- and μ-invariants in Iwasawa theory, between Mordell–Weil groups, Shafarevich–Tate groups, Selmer groups and zeta functions of elliptic curves, and between ideal class groups and regulators of number fields.