Higher Epsilon-Factors for Higher Local Fields

Project Information

HEF

Grant agreement ID: 701679

DOI 10.3030/701679

Project terminated on 30 June 2018

EC signature date 22 February 2016

Start date 17 October 2016

End date 16 October 2018

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost € 159 460,80

EU contribution € 159 460,80

Coordinated by

FREIE UNIVERSITAET BERLIN
Germany

Objective

The goal of this project is to extend the work of Beilinson-Bloch-Esnault (BBE) on de Rahm epsilon-factors in dimension one to higher local fields. Together with my collaborators Oliver Braunling and Jesse Wolfson we have carefully studied one of the main tools of BBE, Tate vector bundles, in an abstract context which allows to handle higher-dimensional situations. Moreover, we have successfully constructed a special case of higher epsilon-factors, called higher-dimensional Contou-Carrère symbols, and established an array of reciprocity laws for this case. It seems very likely that similar methods, also of K-theoretic nature like in the case of symbols, can be used to shed light on higher de Rahm epsilon-factors, and reciprocity phenomena thereof. The candidate will investigate the connection between the approach via Tate objects, and extend Patel's K-theoretic framework in a compatible way. A higher analogue of Beilinson's topological epsilon-factors is also envisioned, and a comparison result between this theory and the de Rham version. This project offers a new viewpoint on the arithmetic and geometric behaviour of higher local fields.

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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.

• natural sciences › mathematics › pure mathematics › arithmetics
• social sciences › law

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Keywords

• Epsilon-factors
• flat connections
• holonomic D-modules
• higher local fields
• Tate vector spaces
• K-theory
• reciprocity
• adèles

Programme(s)

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme
• H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility

Topic(s)

• MSCA-IF-2015-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF)

Call for proposal

H2020-MSCA-IF-2015

Funding Scheme

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

Coordinator

FREIE UNIVERSITAET BERLIN

• Net EU contribution: € 159 460,80
• Address: KAISERSWERTHER STRASSE 16-18 ; 14195 Berlin ; Germany
• Region: Berlin › Berlin › Berlin
• Activity type: Higher or Secondary Education Establishments
• Total cost: € 159 460,80