On explicit reciprocity laws for the local Carlitz-Kummer symbols
type: Item
instance of: scholarly article
title: On explicit reciprocity laws for the local Carlitz-Kummer symbols
zbMATH Open document ID: 0937.11020
author: Bruno Anglès
published in: Journal of Number Theory
publication date: 2000-06-01T00:00:00Z
review text: Following the main steps of the proof of Wiles explicit formula [\textit{A. Wiles}, Higher explicit reciprocity laws, Ann. Math. (2) 107, 235-254 (1978; Zbl 0378.12006)] for the generalized Hilbert symbol, it is easy to show that its analogue holds for Lubin-Tate formal groups in positive characteristic. The paper does this in the partial case where isogeny is a so called Carlitz polynomial. The text contains many misprints.
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 11S31
zbMATH DE Number: 1375089
zbMATH Keywords: Wiles explicit formula
zbMATH Keywords: Lubin-Tate formal groups in positive characteristic
zbMATH Keywords: Carlitz polynomial
zbMATH Keywords: reciprocity laws
reviewed by: I. B. Fesenko
MaRDI profile type: Publication
full work available at URL: jnth.1999.2403
OpenAlex ID: W1996298761
cites work: On the orthogonal of cyclotomic units in positive characteristic
cites work: Q4714153
cites work: Explicit Class Field Theory for Rational Function Fields
cites work: Q3995821
cites work: Carlitz-Kummer function fields
cites work: Local and global residue symbols for algebraic function fields
cites work: Higher explicit reciprocity laws
DOI: 10.1006/JNTH.1999.2403
description: scientific article; zbMATH DE number 1375089