Jakob Scholbach

Professore Asscociato, Dipartimento di Matematica, Università degli Studi di Padova
email: jakob.scholbach@unipd.it
Mail: Via Trieste 63, 35121 Padova, Italy
Office: 5th floor, part BC

Research

I am interested in motives, the Langlands program, special L-values, abstract homotopy theory, and Arakelov theory. The following papers are also available via the arxiv, Orcid, Google scholar, zbMath, or MathSciNet.

• 22. Central motives on parahoric flag varieties, joint work with Robert Cass and Thibaud van den Hove.
• 21. Frobenius rigidity in 𝔸¹-homotopy theory, Documenta Mathematica (to appear), joint work with Timo Richarz
• 20. The geometric Satake equivalence for integral motives, joint work with Robert Cass and Thibaud van den Hove. An Oberwolfach report by van den Hove on this article can be found here.
• 19. The motivic Satake equivalence and a question about the Drinfeld lemma, Oberwolfach Reports
• 18. Integral Motivic Sheaves And Geometric Representation Theory, Advances in Mathematics (2023); joint work with Jens Eberhardt
• 17. Constructible sheaves on schemes, Advances in Mathematics (2023), Vol. 429, 46 pp., joint work with Tamir Hemo and Timo Richarz. Here are notes of a talk on this and the next paper.
• 16. A categorical Künneth formula for constructible Weil sheaves, Algebra and Number theory (2024), Vol. 18, n. 3, 38 pp., joint work with Tamir Hemo and Timo Richarz
• 15. Tate motives on Witt vector affine flag varieties, Selecta Mathematica (2021), Vol. 27, 34 pp., joint work with Timo Richarz
• 14. The motivic Satake equivalence, Mathematische Annalen (2021), 59 pages, joint work with Timo Richarz
• 13. The intersection motive on the moduli stack of shtukas, Forum of Mathematics Sigma (2020), Vol. 8 (e8), pp. 1–99, joint work with Timo Richarz; Corrigendum
• 12. Motives and homotopy theory, Habilitation thesis, See the first section for a general audience introduction to many of the papers below.
• 11. Homotopy theory of symmetric powers, Homology, Homotopy and Applications (2018), Vol. 20 (1), pp. 359–397, joint work with Dmitri Pavlov
• 10. Admissibility and rectification of colored symmetric operads, Journal of Topology (2018), Vol. 11, pp. 559–601, joint work with Dmitri Pavlov
• 9. Symmetric operads in abstract symmetric spectra, Journal of the Institute of Mathematics of Jussieu (2018), pp. 1–52, joint work with Dmitri Pavlov
• 8. Arakelov motivic cohomology II, Journal of Algebraic Geometry (2015), Vol. 24, pp. 755–786
• 7. Algebraic K-theory of the infinite place, Journal of Homotopy and Related Structures (2015), Vol. 10 (4), pp. 821–842
• 6. Arakelov motivic cohomology I, Journal of Algebraic Geometry (2015), Vol. 24, pp. 719–754, joint work with Andreas Holmstrom
• 5. Mixed Artin-Tate motives over number rings, Journal of Pure and Applied Algebra (2011), Vol. 215, pp. 2106–2118, published version contains sections 1–4 of the preprint, only
• 4. Special L-values of geometric motives, Asian Journal of Mathematics (2017), Vol. 21 (2) pp. 225–264
• 3. f-cohomology and motives over number rings, Kodai Mathematical Journal (2012), Vol. 35, pp. 1–32
• 2. Special L-values of motives, PhD Thesis, Advisor: Annette Huber, Universität Freiburg
• 1. Geometric motives and the h-topology, Mathematische Zeitschrift (2012), Vol. 272, pp. 956–986, Corrigendum

Teaching

Office hours: anytime via zoom, please email me

Past courses

• Homology and Cohomology (Spring 2024)
• Category theory (WS 2021/22)
• Komplexe Zahlen, Quaternionen und andere Zahlenbereiche (Algebra für Lehramtsstudierende, WS 2020/21)
• Algebraische Topologie für Lehramtsstudierende (SS 2020)
• Darstellungstheorie endlicher Gruppen (WS 2018/19)
• Riemannsche Flächen (WS 2017/18)

Organization

• I am the coordinating the MSCA Doctoral Network REMOLD - Representations, Motives and Langlands Duality
• Representation theory's hidden motives (September 2021)