Research Grant PN-II-ID-PCE-2012-4-0640
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Program: IDEI
Financed by: UEFISCDI
Project type: Exploratory Research Project
Contract: 67 from 02/09/2013
Project code: PN-II-ID-PCE-2012-4-0640
Project title: Combinatorial and geometric methods for studying arithmetic invariants
Project director: Prof. dr. Răzvan Dinu LIŢCANU, University „Alexandru Ioan Cuza” of Iaşi
Duration: 2013-2016
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Project summary:
Arithmetic geometry provides an appropriate, sophisticate and stimulating context for formulating most of the classical and modern problems in number theory. The central objective of this proposal is obtaining new results in arithmetic geometry and, more specifically, in Arakelov theory, which concern arithmetic numerical invariants and characteristic classes. A special attention will be given to explicit methods and techniques. The specific objectives of the proposal belong to three major research tasks:
1. Heights in arithmetic geometry and relations with other arithmetic invariants. Height functions will be constructed by means of more explicit and combinatoric methods, as an interplay between Belyi’s theorem and Arakelov theory.
2. Arithmetic intersection theory and height functions on algebraic stacks. For studying and computing height functions on moduli spaces one needs to extend fundamental results in Arakelov theory to algebraic stacks.
3. Arithmetic Grothendieck-Riemann-Roch formulae for general projective morphisms and applications in the study of height functions.
One of the priorities of the project is the development of the interaction of the members of the team with other researchers at European and international level.