4 papers · 1 filter
Fibration theorems for varieties with the weak Hilbert property
Sebastian Petersen
The weak Hilbert property (WHP) for varieties over fields of characteristic zero was introduced by Corvaja and Zannier in 2017. There exist integral variants of WHP for arithmetic…
Ranks of abelian varieties and the full Mordell-Lang conjecture in dimension one
Arno Fehm, Sebastian Petersen
Let be a non-zero abelian variety over a field that is not algebraic over a finite field. We prove that the rational rank of the abelian group is infinite when i…
On the semisimplicity of reductions and adelic openness for -rational compatible systems over global function fields
Gebhard Böckle, Wojciech Gajda, Sebastian Petersen
Let be a normal geometrically connected variety over a finite field of characteristic~. Let be a number field. Using automorphic methods over global function fields,…
On varieties of Hilbert type
Lior Bary-Soroker, Arno Fehm, Sebastian Petersen
A variety X over a field K is of Hilbert type if the set of rational points X(K) is not thin. We prove that if f: X\to S is a dominant morphism of K-varieties and both S and all fi…