Project description
Linking arithmetic geometry to derived categories of coherent sheaves
The zeta function of an algebraic variety over a finite field is one of the most widely studied invariants in arithmetic geometry. According to Orlov’s conjecture, the invariant can be detected by the derived category of coherent sheaves on the variety. The EU-funded ZETA-FM project aims to prove this conjecture for large classes of varieties. To achieve this, project researchers will use a wide range of arithmetic geometry techniques with ideas that have classically been used in the study of derived categories. ZETA-FM's results will provide further evidence on the convergence between the fields of arithmetic geometry and the derived categories of coherent sheaves.
Objective
Arithmetic geometry and the study of derived categories of coherent sheaves are two central areas of research in algebraic geometry. Despite their many points of contact, they have until recently remained largely disjoint.
The zeta function of an algebraic variety over a finite field is one of the most studied invariants in arithmetic geometry, and a conjecture of Orlov predicts that this invariant can be detected by the derived category of coherent sheaves on the variety. In this project, I will prove this for large classes of varieties.
To achieve this, I will enrich a wide range of techniques from arithmetic geometry with ideas that have classically been used in the study of derived categories. In this way, this project will also serve as a catalyst for further interaction between arithmetic geometry and derived categories.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
You need to log in or register to use this function
Programme(s)
Funding Scheme
ERC-COG - Consolidator GrantHost institution
1012WX Amsterdam
Netherlands