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Open problems in algebraic geometry. (English) Zbl 1009.11002

The 21 open problems presented here were collected on the occasion of a workshop of Arithmetic Geometry at the University of Utrecht, 26-30 June, 2000.
The subjects involved are: curves, Abelian varieties, moduli spaces, \(p\)-divisible groups, Hilbert modular forms, rigid geometry, group schemes, Neron model, \(K3\) surfaces, Calabi-Yau varieties, sporadic groups, knot-invariants.

MSC:

11-02 Research exposition (monographs, survey articles) pertaining to number theory
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11G10 Abelian varieties of dimension \(> 1\)
11G18 Arithmetic aspects of modular and Shimura varieties
14J28 \(K3\) surfaces and Enriques surfaces
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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