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Foundations of Motivic Real K-Theory

Objective

Quadratic forms are ubiquitous throughout mathematics, playing a fundamental role in areas from arithmetic through algebra and geometry. In surgery theory, quadratic forms feature prominently in the classification of smooth manifolds in a given homotopy type, while in arithmetic geometry they can be used to encode Galois and motivic cohomology classes via Milnor's conjecture. The theory of quadratic forms is naturally very sensitive to the prime 2. While in surgery theory this effect is critical, in algebraic geometry it was often set aside by assuming 2 to be invertible in all ground rings. A recent joint work of the PI and collaborators on the foundations of Hermitian K-theory uses state-of-the-art tools from higher category theory to develop a new framework for the subject, bringing a bordism theoretical approach to the algebraic study of quadratic forms, all while accommodating for the subtleties posed by the prime 2.
Building on this recent success, the project MRKT aims to remove the theoretical barrier of the prime 2 from the study of Hermitian K-theory in the domain of algebraic geometry, and set up the foundations of motivic Hermitian K-theory and real algebraic K-theory over the integers.

Call for proposal

ERC-2020-STG
See other projects for this call

Funding Scheme

ERC-STG - Starting Grant

Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Address
Rue Michel Ange 3
75794 Paris
France
Activity type
Research Organisations
EU contribution
€ 1 331 091

Beneficiaries (1)

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France
EU contribution
€ 1 331 091
Address
Rue Michel Ange 3
75794 Paris
Activity type
Research Organisations