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.
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.
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
@article{AIF_2008__58_6_2075_0, author = {del Angel, Pedro Luis and M\"uller-Stach, Stefan}, title = {Differential {Equations} associated to {Families} of {Algebraic} {Cycles}}, journal = {Annales de l'Institut Fourier}, pages = {2075--2085}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {6}, year = {2008}, doi = {10.5802/aif.2406}, mrnumber = {2473629}, zbl = {1151.14009}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2406/} }
TY - JOUR AU - del Angel, Pedro Luis AU - Müller-Stach, Stefan TI - Differential Equations associated to Families of Algebraic Cycles JO - Annales de l'Institut Fourier PY - 2008 SP - 2075 EP - 2085 VL - 58 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2406/ DO - 10.5802/aif.2406 LA - en ID - AIF_2008__58_6_2075_0 ER -
%0 Journal Article %A del Angel, Pedro Luis %A Müller-Stach, Stefan %T Differential Equations associated to Families of Algebraic Cycles %J Annales de l'Institut Fourier %D 2008 %P 2075-2085 %V 58 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2406/ %R 10.5802/aif.2406 %G en %F AIF_2008__58_6_2075_0
del Angel, Pedro Luis; Müller-Stach, Stefan. Differential Equations associated to Families of Algebraic Cycles. Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 2075-2085. doi : 10.5802/aif.2406. https://aif.centre-mersenne.org/articles/10.5802/aif.2406/
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