TY - CHAP
T1 - Endomorphisms of ordinary superelliptic jacobians
AU - Zarhin, Yuri G.
N1 - Publisher Copyright:
© 2021 American Mathematical Society.
PY - 2021
Y1 - 2021
N2 - 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[ζℓ ] the ring of integers in the ℓth cyclotomic field, Cf,ℓ: yℓ = 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[ζℓ ] if J(Cf,ℓ ) is an ordinary abelian variety and (ℓ, n) ≠ (5, 5).
AB - 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[ζℓ ] the ring of integers in the ℓth cyclotomic field, Cf,ℓ: yℓ = 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[ζℓ ] if J(Cf,ℓ ) is an ordinary abelian variety and (ℓ, n) ≠ (5, 5).
UR - https://www.scopus.com/pages/publications/85107284679
UR - https://www.scopus.com/pages/publications/85107284679#tab=citedBy
U2 - 10.1090/conm/767/15397
DO - 10.1090/conm/767/15397
M3 - Chapter
AN - SCOPUS:85107284679
T3 - Contemporary Mathematics
SP - 51
EP - 69
BT - Contemporary Mathematics
PB - American Mathematical Society
ER -