arXiv subjects
Publications and source records attributed to Dylon Chow.
We prove a variant of Manin's conjecture for Campana points on wonderful compactifications of semi-simple algebraic groups of adjoint type. We use this to provide evidence for a new conjecture on the leading constant in Manin's conjecture for Campana points.
We give a description of the Picard group of a reductive group over a number field as an abelianized Galois cohomology group. It gives another approach of a result due to Labesse.
Over a global field (number field or function field of a curve over a finite field), theorems for the Galois cohomology of algebraic groups have long been known. For $F$ the function field of a curve over the formal series field $\mathbb{C}((t))$, under an additional assumption on the curve, we establish an explicit description of the localization map in Galois cohomology. This is achieved by extending the theory of $B(F,G)$ due to Kottwitz.
We prove the finiteness of the kernel of the localization map in the Galois cohomology of a connected reductive group over a global field
We study surjectivity of a localization map in Galois cohomology.
We show that for nonarchimedean local fields $F$, the pairing from the algebraic part of the Brauer group of a reductive group $G$ characterizes all continuous homomorphisms from $G(F)$ into $\mathbb{Q}/\mathbb{Z}$. This generalizes results of Loughran and Loughran-Tanimoto-Takloo-Bighash.
We study the asymptotic distribution of S-integral points of bounded height on partial bi-equivariant compactifications of semi-simple groups of adjoint type.