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Triangulated categories and their applications, chiefly to algebraic geometry

There are two components to this project. (1) Develop and extend the striking new theory, created by the PI in the last few years, which studies triangulated categories via metrics and approximations. (2) Build on very rec... ver más

31/08/2027

UMIL

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

UNIVERSITA DEGLI STUDI DI MILANO No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-07-02

ERC-2022-ADG: ERC ADVANCED GRANTS Scope:Objectives

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Cerrada hace 2 años

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Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

1 Participantes

UMIL

1.04M€ | Lider

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Duración del proyecto: 49 meses Fecha Inicio: 2023-07-02
Fecha Fin: 2027-08-31

Líder del proyecto

UNIVERSITA DEGLI STUDI DI MILANO No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 1M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto There are two components to this project. (1) Develop and extend the striking new theory, created by the PI in the last few years, which studies triangulated categories via metrics and approximations. (2) Build on very recent work to better understand which functors are Fourier-Mukai and which aren't. In the case of (1), the novel idea of appropriately using metrics has already allowed the PI to prove several difficult conjectures, the most recent just a few weeks ago. The potential of the new theory is immense, and this project aims to extend the scope of the methods and apply them widely. The project also aims to work out the implications of a surprising theorem proved by the methods, which shows that the derived category of perfect complexes and the bounded derived category of coherent sheaves are constructible from each other, as triangulated categories, by an explicit recipe. This theorem flies in the face of accepted wisdom, which viewed the two categories as totally different. Thus a whole body of work, analysing the many differences between these derived categories, needs to be carefully revisited and reconsidered in the light of the new construction. The Fourier-Mukai transforms of (2) have a long and venerable history, with beautiful work by many authors. But there were novel techniques introduced in a couple of recent articles, and the project plans to deploy them more widely. The aim is for a breakthrough in the area, leading to a better understanding of which exact functors are Fourier-Mukai and which aren't.

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