Differential Equations associated to Families of Algebraic Cycles
[Équations différentielles associées aux familles de cycles algébriques]
del Angel, Pedro Luis1 ; Müller-Stach, Stefan2
1 CIMAT Guanajuato, Mexico (Mexique)
2 Johannes Gutenberg–Universität Mainz Institut für Mathematik Fachbereich 08 (Deutschland)
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.

DOI : 10.5802/aif.2406
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
del Angel, Pedro Luis 1 ; Müller-Stach, Stefan 2

1 CIMAT Guanajuato, Mexico (Mexique)
2 Johannes Gutenberg–Universität Mainz Institut für Mathematik Fachbereich 08 (Deutschland) 
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del Angel, Pedro Luis; Müller-Stach, Stefan. Differential Equations associated to Families of Algebraic Cycles. Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 2075-2085. doi : 10.5802/aif.2406. http://www.numdam.org/articles/10.5802/aif.2406/

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