We present recent anabelian results that ensue the introduction of Artin-Mazur and Friedlander homotopical étale context in arithmetic-geometry by A. Schmidt and J. Stix -- an étale homotopy type reformulation of Mochizuki’s Theorem A, a higher dimensional anabelian result: every point of smooth variety over number fields admits an anabelian Artin neighbourhood (see also Hoshi’s generalization from number to generalized sub-p-adic field for polycurves.) A special attention is given on how classical and homotopical anabelian geometry interact together. In a broader perspective, homotopical geometry provides new insights in arithmetic geometry for example in terms of stacks and motivic homotopy theory.

Programme and Schedule

The seminar takes place every two weeks on Monday 13:30-16:30. See Programme for details and references.

10/17	Talk 0	Arithmetic Geometry: back and forth to Algebraic Topology	B.Collas
11/11	Talk 1	Étale Homotopy Type of Schemes, Higher Homotopy Groups	W.Porowski (1)
11/18	Talk 2	Model Category on Pro-Spaces and Artin-Mazur's (I)	T.Yuji
12/02	Talk 2'	Model Category on Pro-Spaces and Artin-Mazur's (II)	T.Yuji
12/16	Talk 3 & 4	Étale Homotopy Types in Algebraic Geometry & Pointed vs Unpointed pro-Spaces	B.Collas
01/06	Talk 5	A Homotopical Mochizuki Theorem	K.Higashiyama
01/20	Talk 9	Strong Anabelian Zariski Neighbourhoods & Retraction	K.Sawada
02/03	Talk 8	Anabelian Classifying Spaces for pro-Groups	--
02/17	Talk 6	A Weak Anabelian Result	N.Yamaguchi
03/02	Talk 7	Class Preservation and Retraction	K.Sawada
03/16	Talk 10	Relative Anabelian Neighbourhoods & Polycurves	K.Sawada

(1) Moved due to "Bunka no hi". (*) Organizational update due to the participants availability. Due to coronavirus prevention, the seminar will take place as a skype seminar.

Participants

1. Benjamin Collas, RIMS - Kyoto University, JP;
2. Kazumi Higashiyama, RIMS - Kyoto University, JP;
3. Masaoki Mori, Osaka University, JP;
4. Wojciech Porowski, RIMS - Kyoto University, JP/UK;
5. Kenji Sakugawa, RIMS - Kyoto University JP;
6. Koichiro Sawada, RIMS - Kyoto University, JP;
7. Densuke Shiraishi, Osaka, University, JP;
8. Naotake Takao, RIMS - Kyoto University, JP;
9. Naganori Yamaguchi, RIMS - Kyoto University, JP;
10. Yu Yang, RIMS - Kyoto University, JP;
11. Tomoki Yuji, RIMS - Kyoto University, JP;

Additional Information

Skype Seminar [02/29/2020]

Software & Hardware: Skype 8.54.0.85 for Linux Debian 9.12 (max. 50 participants.); Logitech PTZ Pro 2 USB video camera (incl. 3 preset prositions) & Yamaha YVC-330 USB & Bluetooth speakerphone (x1).

Programme Update [10/20/2019]

Talk 2 includes the étale topological realization of a scheme of Barnea and Schlank's A projective model structure on pro-simplicial sheaves, and the relative étale homotopy type, with comparison with Artin-Mazur construction in Pro-HoSp and Isaksen's more explicit model category (see Programme.)

Contact

Would you be interested in attending or giving a talk, please contact the organizer (bcollas@kurims.kyoto-u.ac.jp).

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