The programme of this semester is organized in 7 topics around Grothendieck's conjectures that are (1) the existence of sections and rational points (T1 & T6), and (2) some potential obstructions to anabelian phenomenon (T4 & T5). Our approach follows the étale homotopy type and A1-geometry, whose simplicial and homotopical techniques provides some complementary approaches via higher homotopy groups and cohomology theories.

An additional grounding is provided by 3 seminal arithmetic constructions whose common aspect is the consideration of anabelian constructions in higher dimensions or for higher symmetries.

Programme and Schedule

The seminar takes place by Zoom every two weeks on Wednesday 16:00-19:00, JP time (8:00-11:00, UK time; 9:00-12:00 FR time) -- See Programme for details and references.

06/10	T+	Anabelian Geometry by m-solvability for curves and number fields	Yamaguchi
06/24	T1	Brauer & Étale homotopy type rational obstructions (1/2)	Porowski
07/08		Hurwitz Spaces	Prof. P. Dèbes
07/22	T7	Arithmetic of gerbes	Ishii
08/05	T3a	Good reduction & Ogg-Neron-Shafarevich	Philip
08/26	T3b	Anabelian good reduction for curves	Sawada
09/02	T3c	Anabelian good reduction criterion for polycurves	Nagamachi
09/16	T2	Arithmetic Geometry - open discussion session	Collas
09/23	T1	Brauer & Étale homotopy type rational obstructions (2/2)	Porowski
10/07	T2	Log-compactification of moduli stacks of curves	Prof. F. Kato
10/14	T6*	Etale Homotopy Obstructions and Section Conjectures in Fibrations	Corwin

Due to coronavirus prevention, the seminar takes place as a Zoom seminar. Special Guest Talk; *Special time: 21h-23h (JP)

Participants

1. Benjamin Collas, RIMS - Kyoto University, JP;
2. David Corwin, Berkeley University, US;
3. Pierre Dèbes, Lille University, FR;
4. Tim Holzschuh, RIMS - Heidelberg University, JP/GE;
5. Yu Iijima, Hiroshima University, JP;
6. Shun Ishii, RIMS - Kyoto University, JP;
7. Ippei Nagamachi, Tokyo University, JP;
8. Séverin Philip, Université Grenoble Alpes, FR;
9. Wojciech Porowski, RIMS - Nottingham University, JP/UK;
10. Koichiro Sawada, RIMS - Kyoto University, JP;
11. Densuke Shiraishi, Osaka, University, JP;
12. Naganori Yamaguchi, RIMS - Kyoto University, JP;
13. Tomoki Yuji, RIMS - Kyoto University, JP;

Additional Information

Zoom Seminar

Hardware, Software, and MO for the seminar:

• Hardware: PDF Beamer; XP-PEN Star G640 (Graphic tablet, windows); XP-PEN Star Artist 12 (Graphic tablet, mac OS);
• Software: Microsoft OneNote (Windows); Zoom Whiteboard;
• MO for more interactions: Speaker (Vid ON, Mic ON); Audience (Vid ON, Mic OFF); Many short breaks for questions & comments.

Programme update [09/17/2020]

Because of its intersection with last semester seminar and the 2019 KTGU Talk ``Arithmetic homotopic geometry, towards higher symmetries'', the Talk ``A1-Homotopy theory & Anabelian geometry'' has been replaced.

Contact

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

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