Bloch’s formula for 0-cycles with modulus and higher-dimensional class field theory

Binda, Federico; Krishna, Amalendu; Saito, Shuji

doi:10.1090/jag/792

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Bloch’s formula for 0-cycles with modulus and higher-dimensional class field theory

Authors: Federico Binda, Amalendu Krishna and Shuji Saito
Journal: J. Algebraic Geom. 32 (2023), 323-384
DOI: https://doi.org/10.1090/jag/792
Published electronically: August 29, 2022
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Abstract | References | Additional Information

Abstract: We prove Bloch’s formula for the Chow group of 0-cycles with modulus on a smooth quasi-projective surface over a field. We use this formula to give a simple proof of the rank one case of a conjecture of Deligne and Drinfeld on lisse $\overline {\mathbb {Q}}_{\ell }$-sheaves. This was originally solved by Kerz and Saito in characteristic $\neq 2$.

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Additional Information

Federico Binda
Affiliation: Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
MR Author ID: 1183287
ORCID: 0000-0002-3476-440X
Email: federico.binda@unimi.it

Amalendu Krishna
Affiliation: Department of Mathematics, Indian Institute of Science Bangalore, 560012, India
MR Author ID: 703987
Email: amalenduk@iisc.ac.in

Shuji Saito
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan
MR Author ID: 188665
ORCID: 0000-0002-6914-0242
Email: sshuji@msb.biglobe.ne.jp

Received by editor(s): January 27, 2021
Published electronically: August 29, 2022
Additional Notes: The first author was supported by the DFG SFB/CRC 1085 “Higher Invariants”. The third author was supported by JSPS KAKENHI Grant (15H03606) and the DFG SFB/CRC 1085 “Higher Invariants”
Article copyright: © Copyright 2022 University Press, Inc.

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