Strong Lang-Neron properties for abelian varieties (joint work with A. Tamagawa - RIMS).
Vortrag von Prof. Dr. Anna Cadoret
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 19.03.12 Zeit: 13.15 - 14.45 Raum: Y27H25
Let K be a function field over an algebraically closed field k of characteristic p (p=0 or p>0). The classical Lang-Neron theorem asserts that if an abelian variety A over K contains no non-zero trivial abelian subvariety then A(K) is finitely generated and, in particular, the subgroup of K-rational torsion points Tors(A(K)) is finite. When K is the function field of a smooth proper and connected curve X over k one can ask for stronger statements, namely, whether the set of all points P in Tors(A(\overline{K})) (of order prime-to-p) such that the genus (resp. the k-gonality) of the residue field K(P) at P is less than a given g (resp. \gamma) is finite. This is what we call strong Lang-Neron properties.