The bigger Brauer group and twisted sheaves

Heinloth, Jochen; Schröer, Stefan

doi:10.1016/j.jalgebra.2009.04.043

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…Then

scriptG

is an algebraic stack over k (cf. [20, Proposition 1.1]). In this case, any quasi‐coherent sheaf

scriptF

scriptG

admits a left action of

G_{m}

which comes from the left

O_{G}

‐module structure.…”

Section: Embedding Problem Over Root Stacksmentioning

confidence: 99%

An embedding problem for finite local torsors over twisted curves

Otabe

2021

Mathematische Nachrichten

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In his previous paper, the author proposed as a problem a purely inseparable analogue of the Abhyankar conjecture for affine curves in positive characteristic and gave a partial answer to it, which includes a complete answer for finite local nilpotent group schemes. In the present paper, motivated by the Abhyankar conjectures with restricted ramifications due to Harbater and Pop, we study a refined version of the analogous problem, based on a recent work on tamely ramified torsors due to Biswas–Borne, which is formulated in terms of root stacks. We study an embedding problem to conclude that the refined analogue is true in the solvable case.

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“…Then

scriptG

is an algebraic stack over k (cf. [20, Proposition 1.1]). In this case, any quasi‐coherent sheaf

scriptF

scriptG

admits a left action of

G_{m}

which comes from the left

O_{G}

‐module structure.…”

Section: Embedding Problem Over Root Stacksmentioning

confidence: 99%

An embedding problem for finite local torsors over twisted curves

Otabe

2021

Mathematische Nachrichten

View full text Add to dashboard Cite

show abstract

“…Then G is an algebraic stack over k (cf. [20,Proposition 1.1]). In this case, any quasi-coherent sheaf F on G admits a left action of G m which comes from the left O G -module structure.…”

Section: Corollary A7 There Exists a Natural Isomorphismmentioning

confidence: 99%

An embedding problem for finite local torsors over twisted curves

Otabe

2019

Preprint

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In his previous paper, the author proposed as a problem a purely inseparable analogue of the Abhyankar conjecture for affine curves in positive characteristic and gave a partial answer to it, which includes a complete answer for finite local nilpotent group schemes. In the present paper, motivated by the Abhyankar conjectures with restricted ramifications due to Harbater and Pop, we study a refined version of the analogous problem, based on a recent work on tamely ramified torsors due to Biswas-Borne, which is formulated in terms of root stacks. We study an embedding problem to conclude that the refined analogue is true in the solvable case.

show abstract

“…We should also mention that one can construct a larger group, namely the Bigger Brauer group Br(X ), defined by Taylor [Tay82] and adapted to the stack-theoretical setting by Heinloth and Schroer [HS09], where the main difference is that the algebras are not required to have a unit. In their article they prove that if X is a Noetherian Artin stack with quasi-affine diagonal, the equality Br(X ) = H 2 (X , G m ) holds (note that the group on the right need not be torsion).…”

Section: Brauer Group Cohomological Brauer Group Bigger Brauer Groupmentioning

confidence: 99%

The Brauer group of the universal moduli space of vector bundles over smooth curves

Fringuelli¹,

Pirisi²

2018

Preprint

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We compute the Brauer group of the universal moduli stack of vector bundles on (possibly marked) smooth curves of genus at least three over the complex numbers. As consequence, we obtain an explicit description of the Brauer group of the smooth locus of the associated moduli space of semistable vector bundles, when the genus is at least four. Contents 1 Preliminaries about the Brauer group of an Artin stack. 4 1.1 Brauer group, Cohomological Brauer group, Bigger Brauer group . . . . . . . . . 4 1.2 Some invariance results .

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The bigger Brauer group and twisted sheaves

Cited by 8 publications

References 16 publications

An embedding problem for finite local torsors over twisted curves

An embedding problem for finite local torsors over twisted curves

An embedding problem for finite local torsors over twisted curves

The Brauer group of the universal moduli space of vector bundles over smooth curves

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