Akio Tamagawa

The Grothendieck conjecture for affine curves

We prove that the isomorphism class of an affine hyperbolic curve defined over a field finitely generated over Q is completely determined by its arithmetic fundamental group. We also prove a similar result for an affine curve defined over a finite field.

A Prime-to-p Version of Grothendieck’s Anabelian Conjecture for Hyperbolic Curves over Finite Fields of Characteristic p > 0

In this paper, we prove a prime-to-p version of Grothendiecks anabelian conjecture for hyperbolic curves over finite fields of characteristic p>0, whose original (full profinite) version was proved by Tamagawa in the affine case and by Mochizuki in the proper case.

Abelian Surfaces Good Away From 2

Fix a number field

On the arithmetic of abelian varieties

k

Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups

and a rational prime

The Eisenstein Quotient of the Jacobian Variety of a Drinfeld Modular Curve

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A uniform open image theorem for

. We consider abelian varieties whose

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-adic representations, I

-power torsion generates a pro-

THE ALGEBRAIC AND ANABELIAN GEOMETRY OF CONFIGURATION SPACES

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