Homotopical Arithmetic Geometry Seminar - 7 Topics - 2020

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.

06/10T+Anabelian Geometry by m-solvability for curves and number fieldsYamaguchi
06/24T1Brauer & Étale homotopy type rational obstructions (1/2)Porowski
07/08Hurwitz SpacesProf. P. Dèbes
07/22T7Arithmetic of gerbesIshii
08/05T3aGood reduction & Ogg-Neron-ShafarevichPhilip
08/26T3bAnabelian good reduction for curvesSawada
09/02T3cAnabelian good reduction criterion for polycurvesNagamachi
09/16T2Arithmetic Geometry - open discussion sessionCollas
09/23T1Brauer & Étale homotopy type rational obstructions (2/2)Porowski
10/07T2Log-compactification of moduli stacks of curvesProf. F. Kato
10/14T6*Etale Homotopy Obstructions and Section Conjectures in FibrationsCorwin
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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Research Institute for Mathematical Sciences (RIMS)