On Galois cohomology of unipotent algebraic groups over local fields
In this paper, we give a necessary and sufficient condition for the finiteness of Galois cohomology of unipotent groups over local fields of positive characteristic
math.NT↗
arXiv subjects
Nguyen Duy Tan
Publications and source records attributed to Nguyen Duy Tan.
Embedding problems with local conditions and the admissibility of finite groups
Let $k$ be a field of characteristic $p>0$, which has infinitely many discrete valuations. We show that every finite embedding problem for $\Gal(k)$ with finitely many prescribed local conditions, whose kernel is a $p$-group, is properly solvable. We then apply this result in studying the admissibility of finite groups over global fields of positive characteristic. We also give another proof for a result of Sonn.
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On the essential dimension of unipotent algebraic groups
We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field $k$ which is finitely generated over a perfect field, a smooth unipotent algebraic $k$-group is of essential dimension 0 if and only if it is $k$-split.
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On p-embedding problems in characteristic p
Let K be a valued field of characteristic p>0 with non-p-divisible value group. We show that every finite embedding problem for K whose kernel is a p-group is properly solvable.
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