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Oberseminar WiSe 2009/10 Zusammenfassung des Vortrags von R. N. Kloosterman (HU Berlin)

The average rank of elliptic n-folds

For elliptic curves over number fields it is conjectured that half the curves have rank 1 and half the curves have rank 0. Similarly, if C / Fq  is a curve then it is conjectured the half the elliptic curves over Fq(C ) have rank 0 and half the curves have rank 1. In this talk we show that the situation is different if one considers elliptic curves over Fq (V ), with dim (V )>1.