One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse Q ℓ -sheaves on a smooth variety U over a finite field due to Deligne and Drinfeld. The problem is translated into the language of higher dimensional class field theory over finite fields, which describes the abelian fundamental group of U by Chow groups of zero cycles with moduli.A key ingredient is the construction of a cycle theoretic avatar of refined Artin conductor in ramification theory originally studied by Kazuya Kato.where D runs through all effective Cartier divisors on X with |D| ⊂ X \ U and endow it with the inverse limit topology where C(X, D) is endowed with the discrete
Abstract. We propose a definition of improved Milnor K-groups of local rings with finite residue fields, such that the improved Milnor Ksheaf in the Zariski topology is a universal extension of the naive Milnor K-sheaf with a certain transfer map forétale extensions of local rings. The main theorem states that the improved Milnor K-ring is generated by elements of degree one.
We prove that algebraic K-theory satisfies `pro-descent' for abstract blow-up
squares of noetherian schemes. As an application we derive Weibel's conjecture
on the vanishing of negative K-groups.Comment: 48 pages, final versio
The notion of a tamely ramified covering is canonical only for curves. Several notions of tameness for coverings of higher dimensional schemes have been used in the literature. We show that all these definitions are essentially equivalent. Furthermore, we prove finiteness theorems for the tame fundamental groups of arithmetic schemes.
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