Weighted Completion of Galois Groups and Galois Actions on the Fundamental Group of P1- {0,1, ∞}
نویسندگان
چکیده
منابع مشابه
Weighted completion of Galois groups and Galois actions on the fundamental group
Fix a prime number l. In this paper we prove a conjecture [16, p. 300], which Ihara attributes to Deligne, about the action of the absolute Galois group on the pro-l completion of the fundamental group of the thrice punctured projective line. It is stated below. Similar techniques are also used to prove part of a conjecture of Goncharov [11, Conj. 2.1], also about the action of the absolute Gal...
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Fix a prime number l. In this paper we prove l-adic versions of two related conjectures of Deligne, [4, 8.2, p. 163] and [4, 8.9.5, p. 168], concerning mixed Tate motives over the punctured spectrum of the ring of integers of a number field. We also prove a conjecture [11, p. 300], which Ihara attributes to Deligne, about the action of the absolute Galois group on the pro-l completion of the fu...
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The goal of this paper is to provide background, heuristics and motivation for several conjectures of Deligne [12, 8.2, p. 163], [12, 8.9.5, p. 168] and [23, p. 300] and Goncharov [15, Conj. 2.1], presumably along the lines used to arrive at them. A complete proof of the third and fourth of these conjectures and partial solutions of the first two are given in [19]. A second goal of this paper i...
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We study the fundamental group of the Galois closure Xgal of a generic projection from a surface X. Originally, it was believed that π1(Xgal) gives rise to new invariants of X. However, in all examples this group is surprisingly simple. In this article, we offer an explanation for this phenomenon: We compute a quotient of π1(Xgal) that depends on π1(X) and data from the generic projection only....
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2003
ISSN: 0010-437X
DOI: 10.1023/b:comp.0000005077.42732.93