An asymptotic bound for the genus of pointless curves
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  • An asymptotic bound for the genus of pointless curves

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Speaker: Claudio Stirpe (Università di Roma "Sapienza")

Date/Time: 28 February 2012, Tuesday, 11:00

Place: Sabanci University, FENS 2008

Title: An asymptotic bound for the genus of pointless curves

Abstract: The problem of finding a non singular curve of genus g_n without points of degree smaller than n was already studied when the genus is small (compared to the size of the finite field GF(q) ). A construction of a family of curves without points of degree smaller than n was carried out by Clark and Elkies. The genus of such curves is bounded by g_n<n*q^n for large n. In this talk I give a construction of a family of curves over the finite field GF(q) without points of degree smaller than n and of genus smaller than q^n.