Search

We describe generators of disguised residual intersections in any commutative Noetherian ring. It is shown that, over Cohen–Macaulay rings, the disguised residual intersections and algebraic residual intersections are the same, for ideals with sliding depth. This coincidence provides structural results for algebraic residual intersections in a quite general setting. It is shown how the DG-algebra structure of Koszul homologies affects the determination of generators of residual intersections. It is shown that the Buchsbaum–Eisenbud family of complexes can be derived from the Koszul–Čech spectral sequence. This interpretation of Buchsbaum–Eisenbud families has a crucial rule to establish the above results.

We assume the validity of the equivariant Tamagawa number conjecture for a certain motive attached to an abelian extension K/k of number fields, and we calculate the Fitting ideal of the dual of clK− as a Galois module, under mild extra hypotheses on K/k. This builds on concepts and results of Tate, Burns, Ritter and Weiss. If k is the field of rational numbers, our results are unconditional.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Residual intersections are Koszul–Fitting ideals

Determining Fitting ideals of minus class groups via the equivariant Tamagawa number conjecture

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Residual intersections are Koszul–Fitting ideals

Determining Fitting ideals of minus class groups via the equivariant Tamagawa number conjecture