42 citations · 119 across the 37 of their papers we have counts for
11 papers · 1 filter
Mirror symmetry, mixed motives and
Minhyong Kim, Wenzhe Yang
In this paper, we present an application of mirror symmetry to arithmetic geometry. The main result is the computation of the period of a mixed Hodge structure, which lends evidenc…
Fundamental groups and Diophantine geometry
Minhyong Kim
We give a brief exposition on the uses of non-commutative fundamental groups for the study of Diophantine problems via a non-abelian Albanese map.
Motivic L-Functions
Minhyong Kim
This is the text of an introductory lecture delivered at the IHES summer school on motives in July, 2006.
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…
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.