Zeitplan

SCHEDULE

Freitag, 10.12.2021

Time Speaker Title
11:30 - 12:30  Stefan Kebekus (Freiburg) Brauer-Manin obstruction on a simply connected fourfold and a Mordell theorem in the orbifold setting
12:30 - 14:30  Mittagspause
14:30 - 15:30  Angela Ortega (HU Berlin)

Global injectivity of the Prym for ramified double coverings

15:30 - 16:00 Kaffeepause
16:00 - 17:00 Jochen Heinloth (Duisburg-Essen)

 

 

ABSTRACTS

  • Brauer-Manin obstruction on a simply connected fourfold and a Mordell theorem in the orbifold setting

    Stefan Kebekus (Freiburg)

    Almost one decade ago, Poonen constructed the first examples of algebraic varieties over global fields for which Skorobogatov's etale Brauer-Manin obstruction does not explain the failure of the Hasse principle. By now, several constructions are known, but they all share common geometric features such as large fundamental groups. In this paper, we construct simply connected fourfolds over global fields of positive characteristic for which the Brauer-Manin machinery fails. Contrary to earlier work in this direction, our construction does not rely on major conjectures. Instead, we establish a new diophantine result of independent interest: a Mordell type theorem for Campana's "geometric orbifolds" over function fields of positive characteristic. Along the way, we also construct the first examply of simply connected surface of general type over a global field with a non-empty, but non-Zariski dense set of rational points.

    This is joint work with Jorge Pereira (IMPA) and Arne Smeets (Nijmegen).

  • Global injectivity of the Prym for ramified double coverings

    Angela Ortega (HU Berlin)

    Given a finite morphism between smooth projective curves one can canonically associate it a polarised abelian variety, the Prym variety. This induces a map from the moduli space of coverings to the moduli space of polarised abelian varieties, known as the Prym map.

    It is a classical result that the Prym map for étale double coverings over curves of genus at least 7 is generically injective but never injective (Donagi's tetragonal construction).

    We will show that, unlike the unramified case, the Prym map is injective for ramified double coverings over curves of genus at least 1 and ramified in at least 6 points.

    This is a joint work with J.C. Naranjo.

  • tba

    Jochen Heinloth (Duisburg-Essen)