The number of points N of an elliptic curve over a finite field of q elements satisfies the Hasse bound |N - q - 1| ≤2√q, but not every integer N satisfying this bound occurs as the number of points of an elliptic curve over F_q. Deuring has completely classified the N that occur. It turns out that besides the Hasse inequality, there is also a p-adic condition on N. More generally, one can ask what rational functions occur as the zeta functions of a particular class of algebraic varieties over the finite field F_q. In this talk, I will discuss this kind of inverse problems, starting with Deuring's theorem, and leading up to some open questions.
Donnerstag, den 3. November 2016 um 17.15 Uhr, in INF 205, Hörsaal MATHEMATIKON Donnerstag, den 3. November 2016 at 17.15, in INF 205, Hörsaal MATHEMATIKON
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Dr. G. Battiston