SoSe 24 Oberseminar: Motivic spectra
Time and place: Tuesday 14:14-15:45 in M311 and online
In this seminar, we will present the recent theory of motivic spectra without A¹-invariance. We will prove the universal property of the algebraic K-theory of derived schemes due to Annala and Iwasa; develop the theory of oriented motivic spectra and construct algebraic cobordism as the universal oriented theory; explain the formalism of motivic filtrations giving rise to prismatic, syntomic, and motivic cohomology; prove Poincaré duality and explore applications of the latter, such as the Landweber exact functor theorem and the construction of the category of (non-A¹-invariant) motives with rational coefficients over any derived scheme.
The references are:
- T. Annala, R. Iwasa, Motivic spectra and universality of K-theory
- T. Annala, M. Hoyois, R. Iwasa, Algebraic cobordism and a Conner–Floyd isomorphism for algebraic K-theory
- T. Annala, M. Hoyois, R. Iwasa, Atiyah duality for motivic spectra
If you are interested in attending this seminar, please contact Marc Hoyois or Niklas Kipp.
| Date | Topic |
|---|---|
| 16.04 | Projective and weighted homotopy invariance |
| 23.04 | The Bass fundamental theorem |
| 30.04 | The moduli stack of vector bundles |
| 07.05 | Oriented motivic spectra |
| 14.05 | The universal property of algebraic K-theory |
| 21.05 | — |
| 28.05 | Constructing the J-homomomorphism |
| 04.06 | Algebraic cobordism and the universal orientation |
| 11.06 | The Conner–Floyd isomorphism |
| 18.06 | Motivic filtrations |
| 25.06 | Gysin maps and Atiyah duality |
| 02.07 | Logarithmic cohomology |
| 09.07 | Motivic Landweber exactness |
| 16.07 | Adams decomposition and rational motives |