# RTG-Seminar

The Thursday morning seminar (10:15-11:45 in **WSC-N-U-3.05**) will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs,…) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.

Termin | Vortragende*r | Titel |
---|---|---|

20.10.2022 | – | RTG General Assembly |

27.10.2022 | Dario Weißmann | A functorial approach to the stability of vector bundles |

3.11.2022 | V. Srinivas (Tata Institute) | Grothendieck-Lefschetz and Noether-Lefschetz for the divisor class group |

10.11.2022 | Georg Linden (Wuppertal) | Equivariant vector bundles on the Drinfeld upper half space |

17.11.2022 | V. Srinivas (Tata Institute) | Grothendieck-Lefschetz and Noether-Lefschetz for the divisor class group |

24.11.2022 | V. Srinivas (Tata Institute) | Grothendieck-Lefschetz and Noether-Lefschetz for the divisor class group |

Mon, 28.11.2022, 4-6pmS-U-3.03 |
V. Srinivas (Tata Institute) | Grothendieck-Lefschetz and Noether-Lefschetz for the divisor class group |

1.12.2022 | Dan Clark (Durham/ Münster) | The Geometry of the Unipotent component of the moduli space of Weil-Deligne Representations |

12.1.2023 | Bence Forrás | Integrality of smoothed $p$-adic Artin $L$-functions |

19.1.2023 | reserviert | – |

26.1.2023 | reserviert | – |

2.2.2023 | N. N. | tba |

## Abstracts

### Dario Weißmann: A functorial approach to the stability of vector bundles

Semistability is a property of vector bundles which is functorial under pullback by a finite separable morphism, but this is no longer the case for stability. However, the general stable bundle on a smooth projective curve remains stable after pullback by all finite separable morphisms which are prime to the characteristic. Furthermore, this property defines a large open in the moduli space of bundles. In contrast, a result of Ducrohet and Mehta states that the etale trivializable bundles are dense in the moduli space of bundles, i.e., avoiding the characterstic is essential.

### V. Srinivas (Tata Institute): Grothendieck-Lefschetz and Noether-Lefschetz for the divisor class group

Let $X$ be a normal projective variety over an algebraically closed field of characteristic $0$, and $f\colon X\to {\mathbb P}^n$ a finite morphism. Let $Y=f^{-1}(H)$ be the inverse image of a general hyperplane section. In these lectures, I will sketch proofs (obtained with G. V. Ravindra) of results on the map of divisor class groups ${\rm Cl}(X)\to {\rm Cl}(Y)$, analogous to the “classical” Grothendieck-Lefschetz and Noether-Lefschetz theorems for the Picard groups of smooth projective varieties. As an application, we discuss Kollar’s results on recognizing normal projective varieties from the underlying Zariski topological spaces.