Weighted Completion of Galois Groups and Some Conjectures of Deligne
نویسندگان
چکیده
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 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 [7, Conj. 2.1], also about the action of the absolute Galois group on the fundamental group of the thrice punctured projective line, and which derives from the conjectures of Deligne and Ihara and questions of Drinfeld [5, p. 859]. Ihara’s version of Deligne’s conjecture concerns the outer action
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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