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Title: Endomorphism rings of certain Jacobians in finite characteristic

Abstract

We prove that, under certain additional assumptions, the endomorphism ring of the Jacobian of a curve y{sup l}=f(x) contains a maximal commutative subring isomorphic to the ring of algebraic integers of the lth cyclotomic field. Here l is an odd prime dividing the degree n of the polynomial f and different from the characteristic of the algebraically closed ground field; moreover, n{>=}9. The additional assumptions stipulate that all coefficients of f lie in some subfield K over which its (the polynomial's) Galois group coincides with either the full symmetric group S{sub n} or with the alternating group A{sub n}.

Authors:
 [1]
  1. Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow region (Russian Federation)
Publication Date:
OSTI Identifier:
21205702
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 193; Journal Issue: 8; Other Information: DOI: 10.1070/SM2002v193n08ABEH000673; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTIC FUNCTIONS; MATHEMATICAL LOGIC; POLYNOMIALS

Citation Formats

Zarkhin, Yu G. Endomorphism rings of certain Jacobians in finite characteristic. United States: N. p., 2002. Web. doi:10.1070/SM2002V193N08ABEH000673; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Zarkhin, Yu G. Endomorphism rings of certain Jacobians in finite characteristic. United States. https://doi.org/10.1070/SM2002V193N08ABEH000673; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Zarkhin, Yu G. 2002. "Endomorphism rings of certain Jacobians in finite characteristic". United States. https://doi.org/10.1070/SM2002V193N08ABEH000673; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21205702,
title = {Endomorphism rings of certain Jacobians in finite characteristic},
author = {Zarkhin, Yu G},
abstractNote = {We prove that, under certain additional assumptions, the endomorphism ring of the Jacobian of a curve y{sup l}=f(x) contains a maximal commutative subring isomorphic to the ring of algebraic integers of the lth cyclotomic field. Here l is an odd prime dividing the degree n of the polynomial f and different from the characteristic of the algebraically closed ground field; moreover, n{>=}9. The additional assumptions stipulate that all coefficients of f lie in some subfield K over which its (the polynomial's) Galois group coincides with either the full symmetric group S{sub n} or with the alternating group A{sub n}.},
doi = {10.1070/SM2002V193N08ABEH000673; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
url = {https://www.osti.gov/biblio/21205702}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 8,
volume = 193,
place = {United States},
year = {Sat Aug 31 00:00:00 EDT 2002},
month = {Sat Aug 31 00:00:00 EDT 2002}
}