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BogomolovMultiplier SIGNED

Bogomolov Multiplier

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

BogomolovMultiplier project word cloud

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

algebras cohomology implication representations understand group invariants link theory intentions ekedahl strengthen kang expressible akin visible lie behavior noted nontrivial multiplier coclass description peyre theoretical prove extensions shown objects p threefold automorphisms invariant explore structure profinite connections dimensional underlying extension shafarevich secondly adic special multipliers relation descriptions look interplay outer abstract see instance thoroughly tate enrich first inspect davydov combinatorial algebraic automorphism kunyavskii intend wish possessing lastly depends unramified dimensions respect class translating geometric groups turn degree bogomolov category

Project "BogomolovMultiplier" data sheet

The following table provides information about the project.

Coordinator	UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA Organization address address: BARRIO SARRIENA S N city: LEIOA postcode: 48940 website: www.ehu.es contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	Spain [ES]
Project website	https://sites.google.com/site/urbanjezernik/
Total cost	158˙121 €
EC max contribution	158˙121 € (100%)
Programme	1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
Code Call	H2020-MSCA-IF-2016
Funding Scheme	MSCA-IF-EF-ST
Starting year	2017
Duration (year-month-day)	from 2017-10-01 to 2019-09-30

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA Organization address address: BARRIO SARRIENA S N city: LEIOA postcode: 48940 website: www.ehu.es contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	ES (LEIOA)	coordinator	158˙121.00

Map

Project objective

This project is dedicated to studying a geometric invariant called the Bogomolov multiplier. The main objectives of the proposed project are threefold.

First of all, we wish to understand how the structure of the Bogomolov multiplier depends on the structure of the underlying group. To this end, we set to inspect the behavior of the Bogomolov multiplier with respect to another group theoretical invariant, the coclass. In turn, this will require thoroughly developing a theory of Bogomolov multipliers associated to profinite groups. A particular instance of these are $p$-adic Lie groups. We aim to enrich our understanding of their Bogomolov multipliers by translating the study to their associated Lie algebras.

Secondly, we are interested in applications of our knowledge about the Bogomolov multiplier. Our focus here will be to strengthen the visible connections between the Bogomolov multiplier and automorphism groups. Kang and Kunyavskii recently noted a link between the Bogomolov multiplier and the Tate-Shafarevich set. This relation is expressible in terms of outer automorphisms of a given group. We aim to prove the implication that groups possessing special outer automorphisms must have nontrivial Bogomolov multipliers. Further evidence of this interplay between automorphisms and Bogomolov multipliers can be seen in the category of representations of a given group as shown by Davydov, and we intend to look into these more abstract aspects as well.

Lastly, we propose to explore some extensions of the Bogomolov multiplier to higher dimensions. Our intentions here are to find algebraic descriptions of higher dimensional unramified cohomology groups and of Ekedahl invariants akin to the combinatorial description of the Bogomolov multiplier. Peyre has shown that this can be achieved for unramified cohomology groups of degree three for a special class of groups. We see a possible extension of these results in terms of higher dimensional combinatorial objects.

Publications

List of publications.
year	authors and title	journal	last update
2019	Jezernik, Urban; SÃ¡nchez, Jonatan Irrationality of generic quotient varieties via Bogomolov multipliers published pages: , ISSN: , DOI:	ArXiv (preprint, submitted to peer re	2020-04-14
2019	Fernandez-Alcober, Gustavo Adolfo; Jezernik, Urban Bogomolov multipliers of p-groups of maximal class published pages: , ISSN: 0033-5606, DOI:	The Quarterly Journal of Mathematics (accepted for publication, to a	2020-04-14
2018	Jezernik, Urban Verjetnost komutiranja published pages: 121â€“137, ISSN: 0473-7466, DOI:	Obzornik za matematiko in fiziko 65	2020-04-14
2019	Delizia, Costantino; Jezernik, Urban; Moravec, Primoz; Nicotera, Chiara Gaps in probabilities of satisfying some commutator-like identities published pages: , ISSN: 0021-2172, DOI:	Israel Journal of Mathematics (accepted for publication, to a	2020-04-14

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