Endomorphism rings of certain Jacobians in finite characteristic

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Abstract

We prove that, under certain additional assumptions, the endomorphism ring of the Jacobian of a curve yl = 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 Sn or with the alternating group An.

Original languageEnglish (US)
Pages (from-to)1139-1149
Number of pages11
JournalSbornik Mathematics
Volume193
Issue number7-8
DOIs
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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