Cosimplicial objects in algebraic geometry ,

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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Communication dans un congrès
Aigebraic K-Theory and Aigebraic Topology, Lake Louise, Alberta, Canada December 12-16, 1991 , Dec 1991, Lake Luis, Canada. 1993, Algebraic K-Theory and Algebraic Topology
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https://hal.archives-ouvertes.fr/hal-01293611
Contributeur : Zdzislaw, Jozef Wojtkowiak <>
Soumis le : vendredi 25 mars 2016 - 10:10:08
Dernière modification le : jeudi 31 mars 2016 - 15:30:08

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  • HAL Id : hal-01293611, version 1

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Zdzislaw, Jozef Wojtkowiak. Cosimplicial objects in algebraic geometry ,. Aigebraic K-Theory and Aigebraic Topology, Lake Louise, Alberta, Canada December 12-16, 1991 , Dec 1991, Lake Luis, Canada. 1993, Algebraic K-Theory and Algebraic Topology. 〈hal-01293611〉

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