activity
20192026
collaborators

5 papers

math.NT2026

Cohomological Obstructions for Varieties over -adic Function Fields

Yisheng Tian

We introduce various cohomological obstructions for smooth integral varieties over -adic function fields. We show that the unramified obstruction is the finest one among obstruc…

math.AG2026

A Simpler Approach to a Descent Conjecture of Wittenberg

Yisheng Tian

A descent conjecture of Wittenberg [Wit24, Conjecture 3.7.4] predicts that if all the twists of a rationally connected torsor over a smooth base satisfy weak approximation with Bra…

math.NT2022

A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation

Yisheng Tian

We show that certain Tate--Shafarevich groups are unramified which enables us to give an obstruction to the Hasse principle for torsors under tori over p-adic function fields.

math.NT2019

Poitou--Tate sequence for complex of tori over -adic function fields

Yisheng Tian

We complete the picture of local and global arithmetic duality theorems for short complexes of finite Galois modules and tori over -adic function fields. In view of the duality…

math.NT2019

Obstructions to weak approximation for reductive groups over -adic function fields

Yisheng Tian

We establish arithmetic duality theorems for short complexes associated to reductive groups over -adic function fields. Using dualities, we deduce obstructions to weak approxima…