Differential Equations associated to Families of Algebraic Cycles

del Angel, Pedro Luis; Müller-Stach, Stefan

Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 2075-2085.

Nous développons une théorie d’équations associées aux familles de cycles algébriques dans des groupes de Chow supérieurs. Ce formalisme est lié au type inhomogène d’équations de Picard-Fuchs. Pour les familles de surfaces K3 l’équation différentielle ordinaire non-linéaire est semblable à l’équation de Chazy.

We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.

Classification : 14C25, 19E20
Keywords: Higher Chow group, Picard-Fuchs operator, normal function, differential equation
Mot clés : groupe de Chow supérieur, opérateur de Picard-Fuchs, fonction normale, équation différentielle

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