Families of absolutely simple hyperelliptic jacobians

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We prove that the jacobian of a hyperelliptic curve y2 = (x - t)h(x) has no non-trivial endomorphisms over an algebraic closure of the ground field K of characteristic zero if t ∈ K and the Galois group of the polynomial h(x) over K is an alternating or symmetric group on deg(h) letters and deg(h) is an even number greater than 8. (The case of odd deg(h) > 3 follows easily from previous results of the author.)

Original languageEnglish (US)
Pages (from-to)24-54
Number of pages31
JournalProceedings of the London Mathematical Society
Volume100
Issue number1
DOIs
StatePublished - Jan 1 2010

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Hyperelliptic Curves
Alternating group
Even number
Galois group
Endomorphisms
Symmetric group
Closure
Odd
Polynomial
Zero
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Families of absolutely simple hyperelliptic jacobians. / Zarkhin, Yuriy G.

In: Proceedings of the London Mathematical Society, Vol. 100, No. 1, 01.01.2010, p. 24-54.

Research output: Contribution to journalArticle

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N2 - We prove that the jacobian of a hyperelliptic curve y2 = (x - t)h(x) has no non-trivial endomorphisms over an algebraic closure of the ground field K of characteristic zero if t ∈ K and the Galois group of the polynomial h(x) over K is an alternating or symmetric group on deg(h) letters and deg(h) is an even number greater than 8. (The case of odd deg(h) > 3 follows easily from previous results of the author.)

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