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edit approved Jul 24, 2013 at 19:37
Daniel Miller
edit approved Jul 24, 2013 at 19:37
Daniel Miller
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By 'work' I would like the correspondence between fiber functors (to finitely generated projective modules) and algebraic groups to be the same as in the field case.

Specifically, if A$A$ is an affine ring, and if Proj(A)$\operatorname{Proj}(A)$ is the category of finitely generated projective A-modules, when can we say that a fiber functor w:T->Proj(A)$w:\mathcal{T}\to\operatorname{Proj}(A)$ corresponds to an algebraic group over A$A$, where T$\mathcal{T}$ is an A$A$-linear tensor category.

By 'work' I would like the correspondence between fiber functors (to finitely generated projective modules) and algebraic groups to be the same as in the field case.

Specifically, if A is an affine ring, and if Proj(A) is the category of finitely generated projective A-modules, when can we say that a fiber functor w:T->Proj(A) corresponds to an algebraic group over A, where T is an A-linear tensor category.

By 'work' I would like the correspondence between fiber functors (to finitely generated projective modules) and algebraic groups to be the same as in the field case.

Specifically, if $A$ is an affine ring, and if $\operatorname{Proj}(A)$ is the category of finitely generated projective A-modules, when can we say that a fiber functor $w:\mathcal{T}\to\operatorname{Proj}(A)$ corresponds to an algebraic group over $A$, where $\mathcal{T}$ is an $A$-linear tensor category.

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David E Speyer
David E Speyer
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Benjamin Antieau
Benjamin Antieau
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When does Tannakian theory work over affine schemes besides fields?

By 'work' I would like the correspondence between fiber functors (to finitely generated projective modules) and algebraic groups to be the same as in the field case.

Specifically, if A is an affine ring, and if Proj(A) is the category of finitely generated projective A-modules, when can we say that a fiber functor w:T->Proj(A) corresponds to an algebraic group over A, where T is an A-linear tensor category.