Koszul cohomology and support of local cohomology modules of complete intersections

Abstract Let be a Noetherian commutative ring and be a regular sequence in . We introduce a framework to study by linking the Koszul cohomology of on the sequence and local cohomology modules . As an application, we prove that if is a Noetherian regular ring of prime characteristic and form a regular sequence, then is Zariski‐closed for each integer and each ideal .