Because of the attack on the computer network of the University of Duisburg-Essen, the ESAGA site currently can be reached only at https://www.esaga.net/.... Links pointing to https://www.esaga-uni-due.de/ do not work (but one could manually replace uni-due.de by net), and similarly for content, such as images, at such addresses contained in our pages. (Email messages to @uni-due.de addresses are accepted by our mail servers again.)

We apologize for the inconvenience caused by these problems.

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, 4-6pm
S-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.

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

Let $G$ be a split connected reductive group with Lie group $\mathfrak{g}$ and set $q>1$ an integer. Define the Scheme / O $$ S_G( R)= \{(\Phi,N)\in G( R)\times\mathfrak{g}( R)|Ad(\Phi).N=qN\}.$$ This can be interpreted as the unipotent connected component of the moduli space of Weil-Deligne representations valued in G. In this talk, we explore some of the local properties of the irreducible components of this scheme, and of a certain union of irreducible components, and prove that at most points, the subscheme is Cohen-Macaulay.