ERC Starting Grant · 2016
Constructing line bundles on algebraic varieties -- around conjectures of Tate and Grothendieck
The goal of this project is to investigate two conjectures in arithmetic geometry pertaining to the geometry of projective varieties over finite and number fields. These two conjectures, formulated by Tate and Grothendieck in the 1960s, predict which cohomology classes are chern classes of line bundles. They both form an arithmetic counterpart of a theorem of Lefschetz, proved in the 1940s, which itself is the only known case of the Hodge conjecture. These two long-standing conjectures are one of the aspects of a more general web of questions regarding the topology of algebraic varieties which have been emphasized by Grothendieck and have since had a central role in modern arithmetic…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.