Opendata, web and dolomites


Constructing line bundles on algebraic varieties -- around conjectures of Tate and Grothendieck

Total Cost €


EC-Contrib. €






 AlgTateGro project word cloud

Explore the words cloud of the AlgTateGro project. It provides you a very rough idea of what is the project "AlgTateGro" about.

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Project "AlgTateGro" data sheet

The following table provides information about the project.


There are not information about this coordinator. Please contact Fabio for more information, thanks.

 Coordinator Country France [FR]
 Total cost 1˙222˙328 €
 EC max contribution 1˙222˙328 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-12-01   to  2021-11-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITE PARIS-SACLAY FR (SAINT AUBIN) coordinator 1˙222˙328.00


 Project objective

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 geometry. Special cases of these conjectures, appearing for instance in the work of Tate, Deligne, Faltings, Schneider-Lang, Masser-Wüstholz, have all had important consequences.

My goal is to investigate different lines of attack towards these conjectures, building on recent work on myself and Jean-Benoît Bost on related problems. The two main directions of the proposal are as follows. Over finite fields, the Tate conjecture is related to finiteness results for certain cohomological objects. I want to understand how to relate these to hidden boundedness properties of algebraic varieties that have appeared in my recent geometric proof of the Tate conjecture for K3 surfaces. The existence and relevance of a theory of Donaldson invariants for moduli spaces of twisted sheaves over finite fields seems to be a promising and novel direction. Over number fields, I want to combine the geometric insight above with algebraization techniques developed by Bost. In a joint project, we want to investigate how these can be used to first understand geometrically major results in transcendence theory and then attack the Grothendieck period conjecture for divisors via a number-theoretic and complex-analytic understanding of universal vector extensions of abelian schemes over curves.


year authors and title journal last update
List of publications.
2020 Charles, F.
Conditions de stabilité en géométrie birationnelle (d\'après Bridgeland, Bayer-Macrì...)
published pages: tbd, ISSN: , DOI:
Astérisque tbd 2020-03-11
2018 Salim Tayou
On the equidistribution of some Hodge loci
published pages: , ISSN: 0075-4102, DOI: 10.1515/crelle-2018-0026
Journal für die reine und angewandte Mathematik (Crelles Journal) 0/0 2020-03-11
2021 J.-B. Bost
Réseaux euclidiens, séries théta et pentes (d\'après W. Banaszczyk, O. Regev, S. Dadush, N. Stephens-Davidowitz, ...
published pages: tbd, ISSN: , DOI:
Astérisque tbd 2020-03-11

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