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Results tagged with group-schemes
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user 805482
Use this tag for scheme-theoretic and category-theoretic questions about group schemes, as well as those group schemes that are not algebraic groups. A group scheme G over a scheme S is simply a group object in the category of schemes over S. Finite type group schemes over a field are represented by varieties, and considered algebraic groups; for questions specific to algebraic groups use the [algebraic-groups] tag
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Closed subschemes of finite $k$-schemes
in another question (or in Wedhorn's Algebraic Geometry, page 88) it is shown that a subscheme of $k$-schemes of finite type are of finite type again.
Does the same hold closed subschemes of finite $k …
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Group schemes of multiplicative type
I am currently trying to understand the notion of a multiplicative group scheme.
By Milne (https://www.jmilne.org/math/CourseNotes/AGS.pdf, 5.11) it is a group scheme that becomes diagonalizable over …
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Characterisation of Hochschild Cohomology and semi-simple representation
in Demazure-Gabriel "Introduction to Algebraic Geometry and Algebraic Groups" II, §3, 3.7 (Proposition), I do not understand why the implication (iii) -> (i) follows from the result 3.3:
The statement …
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Is the kernel of a morphism of finite group schemes finite?
is the kernel of homorphism of finite group schemes once again finite?
(i.e. if you have $G = Spec A, H = Spec B$ over a field $k$, i.e. $A,B$ finite dimensional $k$-vector spaces, is ker$\varphi$ onc …
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Derivatives of morphisms of linear algebraic groups
I am currently trying to learn about linear algebraic groups and their lie algebra structure.
However, I am struggling to explicitly calculate the derivatives of morphisms between algebraic groups, as …
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Flatness & surjectivity for Group Scheme Morphism
I am currently reading https://arxiv.org/abs/math/0703310 and I was wondering why the map $S \to B_SG''$ in proof of proposition 2.7 (c) is faithfully flat.
This is as far as I already understood thin …
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Hom exact sequence for group representations
in the proof of Proposition II, 3.3.7 (ii) -> (iv) in Demazure-Gabriel "Introduction to Algebraic Geometry and Algebraic Groups", it is stated as obvious that an exact sequence of kG-modules $0 \to V' …
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