Cosimplicial objects in algebraic geometry ,

Zdzislaw, Jozef Wojtkowiak (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Théorie des nombres [math.NT]; Mathématiques [math]; Géométrie algébrique [math.AG]

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. ⟨hal-01293611⟩