Shusuke Otabe
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On Retract Rationality for Finite Connected Group Schemes Open
In the present paper, we prove the retract rationality of the classifying spaces BG for several types of finite connected group schemes G over algebraically closed fields of positive characteristic $$p>0$$ . In particular, we prove the ret…
On retract rationality for finite connected group schemes Open
In the present paper, we prove the retract rationality of the classifying spaces $BG$ for several types of finite connected group schemes $G$ over algebraically closed fields of positive characteristic $p>0$. In particular, we prove the re…
Unramified logarithmic Hodge–Witt cohomology and -invariance Open
Let X be a smooth proper variety over a field k and suppose that the degree map ${\mathrm {CH}}_0(X \otimes _k K) \to \mathbb {Z}$ is isomorphic for any field extension $K/k$ . We show that $G(\operatorname {Spec} k) \to G(X)$ is an isomor…
Unramified logarithmic Hodge-Witt cohomology and $\mathbb{P}^1$-invariance Open
Let $X$ be a smooth proper variety over a field $k$ and suppose that the degree map $\mathrm{CH}_0(X \otimes_k K) \to \mathbb{Z}$ is isomorphic for any field extension $K/k$. We show that $G(\mathrm{Spec} k) \to G(X)$ is an isomorphism for…
On the mod $p$ unramified cohomology of varieties having universally trivial Chow group of zero-cycles Open
Auel-Bigazzi-Böhning-Graf von Bothmer proved that if a proper smooth variety $X$ over a field $k$ of characteristic $p>0$ has universally trivial Chow group of $0$-cycles, the cohomological Brauer group of $X$ is universally trivial as wel…
A generalized Abhyankar's conjecture for simple Lie algebras in characteristic $p>5$ Open
In the present paper, we study a purely inseparable counterpart of Abhyankar's conjecture for the affine line in positive characteristic, and prove its validity for all the finite local non-abelian simple group schemes in characteristic $p…
A generalized Abhyankar's conjecture for simple Lie algebras in characteristic $p>5$ Open
In the present paper, we study a purely inseparable counterpart of\nAbhyankar's conjecture for the affine line in positive characteristic, and\nprove its validity for all the finite local non-abelian simple group schemes in\ncharacteristic…
On a purely inseparable analogue of the Abhyankar conjecture for affine curves Open
Let $U$ be an affine smooth curve defined over an algebraically closed field of positive characteristic. The Abhyankar conjecture (proved by Raynaud and Harbater in 1994) describes the set of finite quotients of Grothendieck’s étale fundam…
Lifting problem for linearly reductive torsors of curves Open
Let $U$ be a smooth relative curve over a complete discrete valuation ring $R$ with algebraically closed residue field $k$ of characteristic $p>0$ which admits a smooth compactification $X$ with $D=X\setminus U$ \'etale over $R$. Let $U_0$…
The tame fundamental group schemes of curves in positive characteristic Open
The tame fundamental group scheme for an algebraic variety is the maximal linearly reductive quotient of Nori's fundamental group scheme. In this paper, we study the tame fundamental group schemes of smooth curves defined over algebraicall…
Liftings of finite linearly reductive torsors of curves in positive characteristic Open
Let $U$ be a smooth curve over a complete discrete valuation ring $R$ with algebraically closed residue field $k$ of characteristic $p>0$ together with a smooth compactification $X$ with $D=X\setminus U$ etale over $R$. Let $U_0$ denote it…
An extension of Nori fundamental group Open
In this paper, we study a certain extension of Nori's fundamental group in the case where a base field is of characteristic 0 and give structure theorems about it. As a result, for a smooth projective curve with genus $g$>1, we prove that …