42 citations · 119 across the 37 of their papers we have counts for
9 papers · 1 filter
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.
Height inequalities and canonical class inequalities
Minhyong Kim
An expository lecture on the analogy between the subjects of the title. Delivered at the International Conference on Number Theory at the Korea Institute for Advanced Study in Dece…
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.
The Hyodo-Kato isomorphism for rational homotopy types
Minhyong Kim, Richard M. Hain
We prove a comparison isomorphism between the De Rham rational homotopy type of a smooth proper log variety defined over a p-adic field and the crystalline rational homotopy type o…
The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrations
Caterina Consani, Minhyong Kim
A conjecture of Kato says that the monodromy operator on the cohomology of a semi-stable degeneration of projective varieties is represented by an algebraic cycle on the special fi…
On the topology of algebraic surfaces and reduction modulo p
Dosang Joe, Minhyong Kim
We observe that the oriented homeomorphism type of a simply- connected smooth projective surface is determined by its algebraic structure modulo an odd prime of good reduction.
Relating decision and search algorithms for rational points on curves of higher genus
Minhyong Kim
For affine plane curves defined over the rationals of genus at least two, we show that a decision algorithm for the existence of solutions also yields a search algorithm for all so…
A vanishing theorem for Fano varieties in positive characteristic
Minhyong Kim
We prove a Kodaira-type vanishing theorem for the Witt vector sheaf on a Fano variety over a perfect field of characteristic p. As a corollary, we deduce that the number of rationa…