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Title:
Galois theory of period and the André-Oort conjecture
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Abstract:
The idea of a Galois theory of periods comes from an insight of Grothendieck. I shall briefly outline of this (conjectural) theory, then sketch the path which led me from it to the AO conjecture, as well as some paths backward. Principally polarized abelian varieties of dimension g are parametrized by the algebraic variety A_g, those with prescribed extra "symmetries" by special subvarieties of A_g, and those with maximal symmetry (complex multiplication) by special points. The AO conjecture characterizes special subvarieties of A_g by the density of their special points. It has been proven last year, after two decades of collaborative efforts putting together many different areas
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