4 papers · 1 filter
The proportion of monogenic orders of prime power indices of the pure cubic field
Minchan Kang, Dohyeong Kim
In this paper, we investigate the proportion of monogenic orders among the orders whose indices are a power of a fixed prime in a pure cubic field. We prove that the proportion is…
Batalin-Vilkovisky formalism in the -adic Dwork theory
Dohyeong Kim, Jeehoon Park, Junyeong Park
The goal of this article is to develop BV (Batalin-Vilkovisky) formalism in the -adic Dwork theory. Based on this formalism, we explicitly construct a -adic dGBV algebra (dif…
Abelian arithmetic Chern-Simons theory and arithmetic linking numbers
Hee-Joong Chung, Dohyeong Kim, Minhyong Kim +3
Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in t…
Integral points on the complement of plane quartics
Dohyeong Kim
Let be the complement of a plane quartic curve defined over a number field. Our main theorem confirms the Lang-Vojta conjecture for when is a generic smooth quartic…