Abstract
Let X be an arc-connected and locally arc-connected topological space and let I be the unit interval. Applying the connected component functor to each fibre of the fibration of the total space map(I, X) over X × X, P(w) = (w(0), w(1)), we get a local system of sets (Poincaré groupoid) over X × X. This construction does not have a straightforward generalization to algebraic varieties over any field. Using cosimplicial objects, we propose a generalization for smooth, algebraic varieties over an arbitrary field of characteristic zero. This leads to a definition of an algebraic fundamental group of De Rham type. We partly calculate the Betti lattice in the algebraic fundamental group for the projective line minus three points.
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© 1993 Springer Science+Business Media Dordrecht
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Wojtkowiak, Z. (1993). Cosimplicial Objects in Algebraic Geometry. In: Goerss, P.G., Jardine, J.F. (eds) Algebraic K-Theory and Algebraic Topology. NATO ASI Series, vol 407. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0695-7_15
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DOI: https://doi.org/10.1007/978-94-017-0695-7_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4302-3
Online ISBN: 978-94-017-0695-7
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