Chow group of 0-cycles with modulus and higher dimensional class field theory

Abstract

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety 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 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.

59 pages, arguments rearranged

References in corpus (2)

• A finiteness theorem for Galois representations of function fields over finite fields (after Deligne)
• Lefschetz theorem for abelian fundamental group with modulus

Cited by in corpus (17)

• Zero cycles with modulus and zero cycles on singular varieties
• Reciprocity sheaves
• Relative cycles with moduli and regulator maps
• Motives with modulus
• A moving lemma for algebraic cycles with modulus and contravariance
• Reciprocity sheaves and their ramification filtrations
• 0-cycles on singular schemes and class field theory
• K-theory and 0-cycles on schemes
• Purity of reciprocity sheaves
• Ramified class field theory and duality over finite fields
• Zero-cycles on normal varieties
• Suslin's moving lemma with modulus
• Derived Log Albanese Sheaves
• Suslin homology of relative curves with modulus
• Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus
• Cycle class maps for Chow groups of zero-cycles with modulus
• Refined Swan conductors mod p of one-dimensional Galois representations