Hyperelliptic jacobians without complex multiplication in positive characteristic

2001/01/06 by Yuri G. Zarhin, Zarhin, Yuri G. · 1 citation
Mathematics · #11G10 #11G30 #14H40 #14K05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G10 #msc:11G30 #msc:14H40 #msc:14K05

paper · pdf · doi:10.48550/arxiv.math/0101050

LaTeX2e, 6 pages

arxiv created 2001/01/06 · arxiv updated 2009/11/30

Abstract

We prove that in odd characteristic the jacobian of a hyperelliptic curve y²=f(x) has no nontrivial endomorphisms over an algebraic closure of the ground field if the Galois group of the polynomial f of even degree is ``very big". The case of characteristic zero was previously treated by the author (Math. Res. Letters 7(2000), 123--132).

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