Seminar on Framed Motives

Meeting time and place:

We meet on Tuesdays,14-16 Uhr (c.t.), in WSC-S-3.14 (Besprechungsraum) (note new time and place)


This semester we will look at the new approach to motivic stable homotopy theory via so-called framed correspondences.


1. (25.10) Maria Yakerson: Introduction. [GP1], [V]. State [GP1, Lemma 5.2], construction given in [An, Definition A.2].

2. (08.11) Andre Chatzistamatiou: Voevodsky's framed correspondences. Statements in [GP1, §2], proofs in [V].

3. (15.11) Gabriele Guzman: Homotopy invariant framed presheaves. I [GP2].

4. (22.11) Marc Levine: Homotopy invariant framed presheaves. II [GP2].

5. (29.11) Wataru Kai: Model structures for simplicial framed presheaves. [GP1, §4]. Additivity theorem. [GP1, §5].

6. (06.12/13.12) Daniel Harrer: The triangulated category of framed motives. [GP1, §6].

7. (20.12) Anandam Banerjee:  Framed presheaves and resolutions for suspension P1-spectra. [GP1, §8, §9].

8. (10.01.2017)  Vladimir Sosnilo: Cancellation theorem [AGP].

9. (17.01.) ???: Framed motives of relative motivic spheres. [GPN].

10. (24.01.) ???: Reconstructing SH(k). [GP1, §10].

11. (31.01.) Maria Yakerson: Connection with Chow-Witt correspondences according to F. Déglise and J. Fasel's notes. [CF]

12. (07.02.) Lorenzo Mantovani: Framed correspondences and Milnor-Witt K-theory. [Ne].




[An] A. Ananyevskiy, On the zeroth stable A1-homotopy group of a smooth curve. arXiv:1606.06210

[AGP] A. Ananyevskiy, G. Garkusha, I. Panin, Cancellation theorem for framed motives of algebraic varieties. arXiv:1601.06642

[CF] B. Calmes, J. Fasel, The category of finite Chow-Witt correspondences. arXiv:1412.2989

[GP1] G. Garkusha, I. Panin, Framed motives of algebraic varieties (after V. Voevodsky). arXiv:1409.4372

[GP2] G. Garkusha, I. Panin, Homotopy invariant preserves with framed transfers. arXiv:1504.00884

[GPN] G. Garkusha, A. Neshitov, I. Panin, Framed motives of relative motivic spheres. arXiv:1604.02732

[Ne] A. Neshitov, Framed correspondences and the Milnor-Witt K-theory. arXiv:1410.7417

[PSV] Panin, Stavrova, Vavilov, On Gorthendieck-Serre's conjecture concerning principal G-bndles over reductive group schemes: I

[V] V. Voevodsky, Notes on framed Correspondences