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CORDIS

Algebraic K-theory -- Arithmetic and Topology

Project description

Building a stronger connection between topological and algebraic K-theory

In mathematics, K-theory is the study of a ring generated by vector bundles over a topological space. In general, there are two main types of K-theory: topological and algebraic. The goal of the EU-funded K-theory project is to find strong connections between these two types. The project will extend prior work which established the foundations of a real algebraic K-theory spectrum that led to a solution of a conjecture of Hesselholt–Madsen. It will also take into account recent results in algebraic K-theory that prove the existence of a ring spectrum – the circle-dot ring – which determines the failure of excision in K-theory.

Objective

Algebraic $K$-theory -- Arithmetic and Topology. The goal of the proposed project is to use recent results in algebraic K-theory to further the connection between algebraic K-theory on the one hand, and arithmetic and topology on the other. This will split the proposed project into two parts: The one exhibiting connections to topology, more precisely the topology of manifolds and Poincaré duality spaces, and the other exhibiting connections to arithmetic geometry, more precisely gaining access at explicit calculations of K-theory groups of (spectral) schemes. Both main goals build on previous work in which I played a role, on the one hand establishing the foundations of a new ``real algebraic K-theory spectrum'' which leads in particular to a solution of a conjecture of Hesselholt--Madsen, and on the other hand a recent result in algebraic K-theory which proves the existence of a ring spectrum, the circle-dot ring, which determines the failure of excision in K-theory. The pure existence (and some formal properties) of this ring have already been exploited for many applications, and the goal of this part of the project is to make the circle-dot ring more explicit and use this new knowledge for explicit computations.

Keywords

Coordinator

KOBENHAVNS UNIVERSITET
Net EU contribution
€ 219 312,00
Address
NORREGADE 10
1165 Kobenhavn
Denmark

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Region
Danmark Hovedstaden Byen København
Activity type
Higher or Secondary Education Establishments
Links
Total cost
€ 219 312,00