Project description
Spaces with noetherian cohomology under study
Cohomology is a field in mathematics that uses algebraic invariants to study geometric objects. Its structural properties reflect the singularities of algebraic varieties and more generally of noetherian schemes. The aim of the EU-funded CohoSing project is to further study spaces with noetherian cohomology. The focus will be on positive and mixed arithmetic settings where perfectoid techniques apply. The project will highlight several interrelated conjectures that would further understanding of basic properties of noetherian schemes.
Objective
The singularities of algebraic varieties and, more generally, Noetherian schemes, tend to be reflected in the structural properties of cohomology. The goal of the project is to study this interplay, with a particular focus on positive and mixed characteristic---arithmetic settings in which the recently developed perfectoid techniques are especially relevant. The project highlights several interrelated conjectures, for instance, purity for flat cohomology, that would further our understanding of basic properties of Noetherian schemes. It proposes to develop the aforementioned interplay further by searching for invariants of singularities in cohomology.
Fields of science
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Funding Scheme
ERC-STG - Starting GrantHost institution
75794 Paris
France