Numerous arithmetico-geometric invariants of spaces have been defined and characterized through the homotopic Galois action. The study of these invariants has driven significant progress in both the diophantine study of abelian varieties through their Tate module and in anabelian geometry as a whole. An important theme in both settings is how the constraints imposed by the Galois action have led to finiteness results - for example the different proofs of Mordell's conjecture.

This workshop focuses on the recent developments surrounding such invariants, with a particular emphasis on the Rasmussen-Tamagawa conjecture. The participants are encouraged to discuss related subjects during the workshop.

Keywords: Diophantine properties, abelian varieties, anabelian properties, Galois action, section conjecture, heavenly property, Rasmussen-Tamagawa conjecture.

※ This event is part of the special year ``Arithmetic, Homotopy, and Geometry 2027-28''.