Endomorphism rings of certain Jacobians in finite characteristic

Journal Article · Sat Aug 31 00:00:00 EDT 2002 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2002V193N08ABEH000673; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21205702

Zarkhin, Yu G ^[1]

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1. Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow region (Russian Federation)

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}.

• OSTI ID: 21205702
• Journal Information: Sbornik. Mathematics, Vol. 193, Issue 8; Other Information: DOI: 10.1070/SM2002v193n08ABEH000673; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

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