Research

Akio Tamagawa is mainly working on covers and fundamental groups of algebraic varieties (especially, curves and their moduli spaces) from the viewpoint of arithmetic geometry. In this direction, he is particularly interested in anabelian geometry and, among other things, he has proved the Grothendieck conjecture for affine curves over finite fields and over fields finitely generated over the rationals. Recently, he is studying various types of refinement of anabelian geometry jointly with Mohamed Saidi; l-adic and modulo l representations of fundamental groups jointly with Anna Cadoret and Chun Yin Hui; a certain finiteness conjecture for abelian varieties (motivated by Yasutaka Ihara's question about the outer Galois representation on the fundamental group of the projective line minus three points) jointly with Christopher Rasmussen; and endomorphism algebras of abelian varieties jointly with Chia-Fu Yu and Valentijn Karemaker.