arXiv subjects

Dao Van Thinh

Publications and source records attributed to Dao Van Thinh.

3 recordsLinked to original sources

arXiv2025

Cohomology of the differential fundamental group of algebraic curves

Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates the relationship between the de Rham cohomology of a vector bundle with connection and the group cohomology of the corresponding representation of the differential fundamental group of X . Consequently, we obtain some vanishing and non-vanishing results for the group cohomology.

math.AG↗

arXiv2018

2-Selmer groups of even hyperelliptic curves over function fields

In this paper, we are going to compute the average size of 2-Selmer groups of families of even hyperelliptic curves over function fields. The result will be obtained by a geometric method which is based on a Vinberg representation of the group $G=\text{PSO}(2n+2)$ and a Hitchin fibration. Consistent with the result over Q of Arul Shankar and Xiaoheng Wang [Rational points on hyperelliptic curves having a marked non-Weierstrass point, in Compos. Math., 154(1):188-222, 2018], we provide an upper bound and a lower bound of the average. However, if we restrict to the family of transversal hyperelliptic curves, we obtain precisely number 6.

math.NT↗

arXiv2017

Average size of 2-Selmer groups of Jacobians of hyperelliptic curves over function fields

In this paper, we are going to compute the average size of 2-Selmer groups of two families of hyperelliptic curves with marked points over function fields. The result will be obtained by a geometric method which could be considered as a generalization of the one that was used previously by Q.P. Ho, V.B. Le Hung, and B.C. Ngo to obtain the average size of 2-Selmer groups of elliptic curves.

math.AG↗