1982
DOI: 10.1007/bf02967978
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The fundamental group-scheme

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Cited by 143 publications
(185 citation statements)
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“…We start with a short review of the notion of a neutral Tannakian category (see, e.g., [13,14,21,25,28] for details). A tensor category is a category C with a bifunctor ⊗ : C × C → C, called the tensor product, two natural isomorphisms A ⊗ (B ⊗ C) → (A ⊗ B) ⊗ C and A ⊗ B → B ⊗ A, for all objects A, B, C of C, called an associativity constraint and a commutativity constraint, satisfying certain axioms (including the pentagon and the hexagon axioms), and with an object ½, called the identity object, and an isomorphism ½ → ½ ⊗ ½, such that ½ ⊗ − : C → C is an equivalence of categories.…”
Section: 4mentioning
confidence: 99%
See 1 more Smart Citation
“…We start with a short review of the notion of a neutral Tannakian category (see, e.g., [13,14,21,25,28] for details). A tensor category is a category C with a bifunctor ⊗ : C × C → C, called the tensor product, two natural isomorphisms A ⊗ (B ⊗ C) → (A ⊗ B) ⊗ C and A ⊗ B → B ⊗ A, for all objects A, B, C of C, called an associativity constraint and a commutativity constraint, satisfying certain axioms (including the pentagon and the hexagon axioms), and with an object ½, called the identity object, and an isomorphism ½ → ½ ⊗ ½, such that ½ ⊗ − : C → C is an equivalence of categories.…”
Section: 4mentioning
confidence: 99%
“…Since a G-equivariant holomorphic principal H-bundle over X × G/P is equivalent to a P -equivariant holomorphic principal H-bundle over X (for the trivial P -action on X), the problem reduces then to studying the dimensional reduction of such bundles over X. To do this we take the Tannakian point of view of Nori [21], regarding a principal H-bundle as a functor from the category of representations of H to the category of vector bundles. To apply this to our situation, we first show in Section 2 that the category of representations of (Q, K) in complex vector spaces has a structure of neutral Tannakian category.…”
Section: Introductionmentioning
confidence: 99%
“…Any finite vector bundle over X is strongly semistable of degree zero. A vector bundle V of degree zero over X is called essentially finite if there is a finite vector bundle E over X and a quotient bundle Q of E of degree zero such that the vector bundle V is a subbundle of Q; see [6], [7]. Essentially finite vector bundles over X form a neutral Tannakian category.…”
Section: Take Any Objectmentioning
confidence: 99%
“…Let G be an affine algebraic group over C. We will briefly recall a reformulation of the definition of principal G-bundles constructed by Nori in [10], [11].…”
Section: The Parabolic Analog Of Principal Bundlesmentioning
confidence: 99%
“…In Proposition 2.9 of [10] (also Proposition 2.9 of [11]) it has been established that the collection of principal G-bundles over X is in bijective correspondence with the collection of functors from Rep(G) to Vect(X) satisfying the abstract properties that the functor F (P ) in (2.1) enjoys. The four abstract properties are described on page 31 of [10], where they are marked F1-F4.…”
Section: The Parabolic Analog Of Principal Bundlesmentioning
confidence: 99%