Endomorphisms of ordinary superelliptic jacobians

Research output: Chapter in Book/Report/Conference proceedingChapter


Let K be a field of prime characteristic p, n ≥ 5 an integer, f (x) an irreducible polynomial over K of degree n, whose Galois group is either the full symmetric group Sn or the alternating group An . Let ℓ be an odd prime different from p, Z[ζ ] the ring of integers in the ℓth cyclotomic field, Cf,ℓ: y = f (x) the corresponding superelliptic curve and J(Cf,ℓ ) its Jacobian. We prove that the ring of all ¯K-endomorphisms of J(Cf,ℓ ) coincides with Z[ζ ] if J(Cf,ℓ ) is an ordinary abelian variety and (ℓ, n) ≠ (5, 5).

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages19
StatePublished - 2021

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • General Mathematics


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