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Algebraic cycles satisfying the Maurer-Cartan equation and the unipotent fundamental group of curves
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- Journal:
- Journal of K-Theory / Volume 11 / Issue 2 / April 2013
- Published online by Cambridge University Press:
- 04 April 2013, pp. 351-392
- Print publication:
- April 2013
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- Article
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We address the question of lifting the étale unipotent fundamental group of curves to the level of algebraic cycles and show that a sequence of algebraic cycles whose sum satisfies the Maurer-Cartan equation would do the job. For any elliptic curve with the origin removed and the curve
, we construct such a sequence of algebraic cycles whose image under the cycle map gives rise to the étale unipotent fundamental group of the curve.
, we construct such a sequence of algebraic cycles whose image under the cycle map gives rise to the étale unipotent fundamental group of the curve.