Ranks of elliptic curves over function fields

2007/11/29 by Lauder, Alan G. B.
#11Y99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0711.4706

Abstract

We present experimental evidence to support the widely held belief that one half of all elliptic curves have infinitely many rational points. The method used to gather this evidence is a refinement of an algorithm due to the author which is based upon rigid and crystalline cohomology.

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