Summary
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.
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| Web resources: | https://cordis.europa.eu/project/id/851146 |
| Start date: | 01-10-2019 |
| End date: | 31-03-2025 |
| Total budget - Public funding: | 1 466 124,00 Euro - 1 466 124,00 Euro |
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Original description
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.Status
SIGNEDCall topic
ERC-2019-STGUpdate Date
27-04-2024
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