Non-supersingular hyperelliptic jacobians

Yuri G. Zarhin

doi:10.24033/bsmf.2477

Non-supersingular hyperelliptic jacobians

Yuri G. Zarhin

Mathematics

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

10 Scopus citations

Abstract

Let K be a field of odd characteristic p, let f(x) be an irreducible separable polynomial of degree n ≥ 5 with big Galois group (the symmetric group or the alternating group). Let C be the hyperelliptic curve y² = f(x) and J(C) its jacobian. We prove that J(C) does not have nontrivial endomorphisms over an algebraic closure of K if either n ≥ 7 or p ≠ 3.

Original language	English (US)
Pages (from-to)	617-634
Number of pages	18
Journal	Bulletin de la Societe Mathematique de France
Volume	132
Issue number	4
DOIs	https://doi.org/10.24033/bsmf.2477
State	Published - 2004

All Science Journal Classification (ASJC) codes

General Mathematics

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10.24033/bsmf.2477

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AB - Let K be a field of odd characteristic p, let f(x) be an irreducible separable polynomial of degree n ≥ 5 with big Galois group (the symmetric group or the alternating group). Let C be the hyperelliptic curve y2 = f(x) and J(C) its jacobian. We prove that J(C) does not have nontrivial endomorphisms over an algebraic closure of K if either n ≥ 7 or p ≠ 3.

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Non-supersingular hyperelliptic jacobians

Abstract

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