6 citations · 10 across the 10 of their papers we have counts for
8 papers · 1 filter
On relative computability for curves
Minhyong Kim
We discuss a rational version of a conjecture of Matiyasevich, Davis, and Putnam on the relative decidability of the finiteness problem for Diophantine equations with respect to th…
The motivic fundamental group of the projective line minus three points and the theorem of Siegel
Minhyong Kim
In this paper, we establish a link between the structure theory of the pro-unipotent motivic fundamental group of the projective line minus three points and Diophantine geometry. I…
Torsion points on modular curves and Galois theory
Kenneth A. Ribet, Minhyong Kim
We outline the proof of a theorem of M. Baker and A. Tamagawa that gives a complete description of the torsion points on a modular curve embedded in its Jacobian using the notion o…
A note on Szpiro's inequality for curves of higher genus
Minhyong Kim
This is a short addendum to a note of Beauville on the subject of the title. We prove an inequality that takes into account the constant part of the Jacobian.
Diophantine equations in two variables
Minhyong Kim
This is an expository lecture on the subject of the title delivered at the Park-IAS mathematical institute in Princeton (July, 2000).
Why everyone should know number theory
Minhyong Kim
This was an expository lecture for the graduate student colloquium at the University of Arizona on the topic of numbers.