Objective
Introduction
Moduli uf algebraic curves and moduli of abelian varieties have completely ditferent aspects. Interplay between these two usually lead to difficult questions. From the complex analytic side, both moduli spaces are relatively well understood. The Schottky problem has been answered and that knowledge in some cases leads to intresting structure. Still many aspects are completely open. I want to study some of the related arithmetic questions.
Statement of the problem
Over the complex numbers. the classes of principally polarized abelian varieties (ppav) of dimension g>4, isogenous to jacobians are not the full moduli space of ppav: the proof uses strongly the fact that the field of complex numbers is uncountable and that isogenies of a ppav are countable. Over countable fields. the question is still open and I will try to find an answer.
Ultimate goal
I hope that this question and its solution lead to new insight in the interplay between these two moduli spaces, giving a better understanding of the Torelli locus. Eventually, I hope to answer arithmetic and geometric questions relating these two fascinating structure.
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.
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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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.
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Funding Scheme
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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.
Coordinator
3508 TA UTRECHT
Netherlands
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