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.