SCHEIDERER, C (1992) QUASI-AUGMENTED SIMPLICIAL SPACES, WITH AN APPLICATION TO COHOMOLOGICAL DIMENSION. JOURNAL OF PURE AND APPLIED ALGEBRA, 81 (3). pp. 293-311. ISSN 0022-4049,
Full text not available from this repository.Abstract
Let S be a locally spectral topological space. Under a minor technical assumption on S (which is empty if S is spectral) it is proved that the sheaf-theoretic cohomological dimension of S is not larger than the combinatorial ('Krull') dimension. To this end a weakening of the notion of augmented simplicial space is studied. A typical example of such a quasi-augmented simplicial space X. --> S is the simplicial space of (finite) specialization chains in a locally spectral space S. It is shown that there are natural inverse and direct image functors between sheaves on X. and sheaves on S which form a topos morphism. The notion of cohomological descent allows to study sheaf cohomology on X. instead of S. Criteria are provided for cohomological descent to hold, which are then applied to give the result announced above.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/54389 |
Actions (login required)
 |
View Item |
