Endomorphism algebras of hyperelliptic jacobians and finite projective lines II

Arsen Elkin; Yuri G. Zarhin

Endomorphism algebras of hyperelliptic jacobians and finite projective lines II

Arsen Elkin
, Yuri G. Zarhin

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove that the jacobian of a hyperelliptic curve y² = f(x) is either absolutely simple or isogenous to a self-product of a CM elliptic curve if deg(f) = q+1 where q is a power prime congruent to 7 modulo 8, the polynomial f(x) is irreducible over the ground field of characteristic zero and its Galois group is L₂(q).

Original language	English (US)
Pages (from-to)	1-23
Number of pages	23
Journal	Journal of the Ramanujan Mathematical Society
Volume	25
Issue number	1
State	Published - Mar 2010

All Science Journal Classification (ASJC) codes

General Mathematics

Cite this

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title = "Endomorphism algebras of hyperelliptic jacobians and finite projective lines II",

abstract = "We prove that the jacobian of a hyperelliptic curve y2 = f(x) is either absolutely simple or isogenous to a self-product of a CM elliptic curve if deg(f) = q+1 where q is a power prime congruent to 7 modulo 8, the polynomial f(x) is irreducible over the ground field of characteristic zero and its Galois group is L2(q).",

author = "Arsen Elkin and Zarhin, \{Yuri G.\}",

note = "Funding Information: ∗The first author was partially supported by the Marie Curie Incoming International Fellowship PIIF-GA-2009-236606.",

year = "2010",

month = mar,

language = "English (US)",

volume = "25",

pages = "1--23",

journal = "Journal of the Ramanujan Mathematical Society",

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publisher = "Ramanujan Mathematical Society",

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T1 - Endomorphism algebras of hyperelliptic jacobians and finite projective lines II

AU - Elkin, Arsen

AU - Zarhin, Yuri G.

N1 - Funding Information: ∗The first author was partially supported by the Marie Curie Incoming International Fellowship PIIF-GA-2009-236606.

PY - 2010/3

Y1 - 2010/3

N2 - We prove that the jacobian of a hyperelliptic curve y2 = f(x) is either absolutely simple or isogenous to a self-product of a CM elliptic curve if deg(f) = q+1 where q is a power prime congruent to 7 modulo 8, the polynomial f(x) is irreducible over the ground field of characteristic zero and its Galois group is L2(q).

AB - We prove that the jacobian of a hyperelliptic curve y2 = f(x) is either absolutely simple or isogenous to a self-product of a CM elliptic curve if deg(f) = q+1 where q is a power prime congruent to 7 modulo 8, the polynomial f(x) is irreducible over the ground field of characteristic zero and its Galois group is L2(q).

UR - https://www.scopus.com/pages/publications/84955276943

UR - https://www.scopus.com/pages/publications/84955276943#tab=citedBy

M3 - Article

AN - SCOPUS:84955276943

SN - 0970-1249

VL - 25

SP - 1

EP - 23

JO - Journal of the Ramanujan Mathematical Society

JF - Journal of the Ramanujan Mathematical Society

IS - 1

ER -

Endomorphism algebras of hyperelliptic jacobians and finite projective lines II

Abstract

All Science Journal Classification (ASJC) codes

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