IRMAR, Université de Rennes 1 & CIMPA, Nice
Date(s) : 29/09/2022 iCal
14 h 30 min - 15 h 30 min
If the situation for fixed q and g going to infinity has been studied for a while, much less was known for g fixed and q going to infinity. As a consequence of Katz-Sarnak theory, we’ll first get for any given g > 0, any ε > 0 and all q large enough, the existence of a curve of genus g over Fq with at least 1 + q + (2g − ε)√q rational points. Then using a distinct method, we get weaker bounds of the form 1 + q + 4 √q − 32 but which are valid for any q > q0, with q0 explicit and g>1.
Campus de Luminy, Marseille