| 19. Oktober | Sascha Orlik | Equivariant vector bundles on Drinfeld upper half space over a finite field. |
| 9. November | Mattio Tiso | Syntomic regulators. In this work we introduce different p-adic cohomology theories with a particular ispiration to the Deligne-Beilinson one in the trascendental situation. We will introduce the concept of regulator map as an "higher cycle map" from the higher Chow groups to cohomology theories that we choose to deal with. Our goal is to develop a p-adic theory introduced by Gros and provide a regulator map for it. Some aspects are still open, but this theory allows us to have a connection between Besser and p-adic étale cohomolgy theories in terms of these regulator maps. |
| 23. November | Laura Voggesberger | Nilpotent Pieces in Bad Characteristic. Let G be a connected reductive algebraic group over an algebraically closed field k, and let Lie(G) be its associated Lie algebra. In his series of papers on unipotent elements in small characteristic, Lusztig defined a partition of the unipotent variety of G. This partition is very useful when working with representations of G. Equivalently, one can consider certain subsets of the nilpotent variety of Lie(G) called pieces. This approach appears in Lusztig’s article from 2011. The pieces for the exceptional groups of type G_2 , F_4 , E_6 , E_7 and E_8 in bad characteristic have not yet been determined. In this talk, I will give an introduction to both definitions of the nilpotent pieces and present a solution to this problem for groups of type G_2 and F_4. |
| 14. Dezember | Olivier Dudas | TBA. |
| 4. Januar | Georg Linden | TBA. |
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Marco d'Addezio | TBA. |
| 25. Januar | Olivier Gregory | Log-motivic cohomology and a deformational semistable $p$-adic Hodge conjecture. Let $k$ be a perfect field of characteristic $p>0$ and let $X$ be a proper scheme over $W(k)$ with semistable reduction. I shall define a logarithmic version of motivic cohomology for the special fibre $X_k$, and relate it to logarithmic Milnor K-theory and logarithmic Hyodo-Kato Hodge-Witt cohomology. The bidegree $(2r,r)$ log-motivic cohomology group can be seen as a log-Chow group $CH^r_{log}(X_k)$; when $r=1$ we recover the log-Picard group $Pic_{log}(X_k)$. Then, by gluing a logarithmic variant of the Suslin-Voevodsky motivic complex to a log-syntomic complex along the logarithmic Hyodo-Kato Hodge-Witt sheaf, I will prove that an element of the $CH^r_{log}(X_k)$ formally lifts to the continuous log-Chow group of X if and only if it is “Hodge” (i.e. its log-crystalline Chern class lands in the $r$-th step of the Hodge filtration of the generic fibre of $X$ under the Hyodo-Kato isomorphism). This simultaneously generalises the semistable $p$-adic Lefschetz $(1,1)$ theorem of Yamashita (which is the case $r=1$), and the deformational $p$-adic Hodge conjecture of Bloch-Esnault-Kerz (which is the case of good reduction). This is joint work with Andreas Langer. NOTE: the seminar will be on zoom. |
| 1. Februar | Veronika Ertl | Integral p-adic cohomology for open and singular varieties. In this talk I will explain a joint result with Johannes Sprang and Atsushi Shiho. Under certain conditions of resolutions of singularities in positive characteristic, we construct a "good" integral p-adic cohomology theory for open and singular varieties, by using a version of Voevodsky's h-topology. I will explain the construction and clarify in which sense our cohomology is a "good" p-adic cohomology theory. I will also touch on the question why a similar approach does ot work in full generaliy without resolutions of singularities. NOTE: the seminar will be in person and also streamed on Zoom. |