Local cohomological dimension and rectified $\mathbb Q$homological depth of complex analytic spaces
Abstract
We show that the sum of the local cohomological dimension and the rectified $\mathbb Q$homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. In the algebraic case this is equivalent to the coincidence of the rectified $\mathbb Q$homological depth with the de Rham depth studied by Ogus, and follows essentially from his work.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.12896
 Bibcode:
 2021arXiv210812896S
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra
 EPrint:
 8 pages