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Triangulated categories and their applications, chiefly to algebraic geometry

Objective

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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Topic(s)

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HORIZON-ERC - HORIZON ERC Grants

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Call for proposal

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(opens in new window) ERC-2022-ADG

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Host institution

UNIVERSITA DEGLI STUDI DI MILANO
Net EU contribution

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.

€ 1 042 645,00
Address
Via Festa Del Perdono 7
20122 Milano
Italy

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Region
Nord-Ovest Lombardia Milano
Activity type
Higher or Secondary Education Establishments
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Total cost

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.

€ 1 042 645,00

Beneficiaries (1)

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