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.
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. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics applied mathematics mathematical physics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
- social sciences law
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
MSCA-IF-EF-ST - Standard EF
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) H2020-MSCA-IF-2016
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
48940 Leioa
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.