arXiv subjects

Haruhisa Nakajima

Publications and source records attributed to Haruhisa Nakajima.

3 recordsLinked to original sources

arXiv2017

Liftings of pseudo-reflection groups of toric quotients of Krull schemes

Let $G$ be an affine algebraic group with a reductive identity component $G^{0}$ acting regularly on an affine Krull scheme $X = {Spec} (R)$ over an algebraically closed field. Let $T$ be an algebraic subtorus of $G$ and suppose that ${Q}(R)^{T}= {Q}(R^{T})$ of quotient fields. We will show: If $G$ is the centralizer of $T$ in $G$, then the pseudo-reflections of the action of $G$ on $R^{T}$ can be lifted to those on $R$.

math.GR↗

arXiv2017

Valuative characterization of central extensions of algebraic tori on Krull domains

For an algebraic torus $T$, the finite central extensions $G$ of $T$ are characterized in terms of ramification theory of regular actions of $G$ on Krull algebras over an algebraically closed base field $K$ of any characteristic.

math.GR↗

arXiv2017

Reduced class groups grafting relative invariants

Consider an equidimensional faithful conical action of an algebraic torus $T$ on an affine normal conical variety $X$ over an algebraically closed field of characteristic zero. Then there exists a finite normal subgroup $N$ of $T$ such that the action of $T$ on $X/N$ is coffee.

math.GR↗