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AlgTateGro SIGNED

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

Total Cost €

EC-Contrib. €

Partnership

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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.

form theoretic algebraic classes universal regarding projective theory 1940s boundedness conjecture chern moduli conjectures appeared geometric donaldson existence hidden lines grothendieck stholz divisors central beno surfaces masser algebraization had theorem sheaves finite formulated seems uuml twisted tate combine k3 proved predict cohomological arithmetic icirc jean directions geometrically questions schemes instance curves direction proof building spaces web lang line objects hodge techniques finiteness vector follows topology extensions understand lefschetz period appearing relate first emphasized counterpart transcendence invariants itself pertaining relevance faltings analytic modern attack myself varieties deligne 1960s certain special geometry cohomology joint bost bundles schneider abelian w

Project "AlgTateGro" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITE PARIS-SUD 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

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITE PARIS-SACLAY UNIVERSITE PARIS-SACLAY Organization address address: IMMEUBLE TECHNOLOGIQUE ENTREE B RTE DE L ORME AUX MERISIERS city: SAINT AUBIN postcode: 91190 website: n.a. contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	FR (SAINT AUBIN)	coordinator	1˙222˙328.00
2	UNIVERSITE PARIS-SUD UNIVERSITE PARIS-SUD Organization address address: RUE GEORGES CLEMENCEAU 15 city: ORSAY CEDEX postcode: 91405 website: www.u-psud.fr contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	FR (ORSAY CEDEX)	coordinator	0.00

Map

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.

Publications

List of publications.
year	authors and title	journal	last update
2020	Charles, F. Conditions de stabilitÃ© en gÃ©omÃ©trie birationnelle (d\'aprÃ¨s Bridgeland, Bayer-MacrÃ¬...) published pages: tbd, ISSN: , DOI:	AstÃ©risque 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 fÃ¼r die reine und angewandte Mathematik (Crelles Journal) 0/0	2020-03-11
2021	J.-B. Bost RÃ©seaux euclidiens, sÃ©ries thÃ©ta et pentes (d\'aprÃ¨s W. Banaszczyk, O. Regev, S. Dadush, N. Stephens-Davidowitz, ... published pages: tbd, ISSN: , DOI:	AstÃ©risque tbd	2020-03-11

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The information about "ALGTATEGRO" are provided by the European Opendata Portal: CORDIS opendata.