Objective
This project proposes a new theory of higher algebraic geometry that unifies and extends derived and spectral algebraic geometry. Using this theory we will shed new light on p-adic cohomology theories such as syntomic cohomology, prismatic cohomology and localized algebraic K-theory. Within this theory we will construct an integral model of the telescopic sphere spectrum that carries rich information about ambidexterity and galois theory in an accessible way. Building on this we will then provide new lower bounds on the size of the p-local stable homotopy groups of spheres.
This project has its roots in the resolution (in the negative) of Ravenel’s telescope conjecture by Hahn, Levy, Schlank and myself and subsequent developments in our understanding of telescopic homotopy theory. Our view is that progress towards a more comprehensive understanding has been frustrated by inadequacies with existing theories of spectral algebraic geometry. Inadequacies we intend to correct.
The proposed research plan is organized into three phases. In phase one we will develop the foundations of a new theory of higher algebraic geometry based on categorical schemes. We will carefully explore the range of phenomena captured within this theory. We will then construct a six functor formalism for quasicoherent sheaves in this setting. In phase two we will investigate the interplay between cohomology theories and geometry within our theory of categorical schemes. This will focus on p-adic cohomology theories (old and new) and the non-linear operations on them that our theory uncovers. In phase three we will study the category of T(n)-local spectra through the geometry of the moduli stack of categorical schemes equipped with integral ambidexterity of height n.
It is our intention to build new bridges between arithmetic geometry and stable homotopy theory in order to pave the way for deeper understanding of telescopic homotopy theory.
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: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2026-STG
See all projects funded under this callHost institution
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.
1165 KOBENHAVN
Denmark
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.