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Weight decompositions on etale fundamental groups | | J.P.Pridham
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30 Jan 2006 | | Subject: | Algebraic Geometry | | Abstract: | Let X be a smooth or proper variety defined over a finite field. The geometric etale fundamental group of X is a normal subgroup of the Weil group, so conjugation gives it a Weil action. We consider the pro-Q_l-algebraic completion of the fundamental group as a non-abelian Weil representation. Lafforgue’s Theorem and Deligne’s Weil II theorems imply that this affine group scheme is mixed, in the sense that its structure sheaf is a mixed Weil representation. When X is smooth, weight restrictions apply, affecting the possibilities for the structure of this group. This gives new examples of groups which cannot arise as etale fundamental groups of smooth varieties. | | Source: | arXiv, math/0510245 | | Services: | Forum | Review | PDF | Favorites | |
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