Under a mild condition, it is proved that the Chow group modulo numerical equivalence is a finite dimensional -vector space, as in the case of smooth projective varieties. Numerical equivalence on local rings is deeply related to that on smooth projective varieties. For example, if Grothendieck'...
Numerical semigroup ringscanonical modulessemidualizing modulesBurch idealsA semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen鈥揗acaulay ringR, the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one...