Flat affine group schemes
WebMar 3, 2016 · We establish a duality between flat affine group schemes and rigid tensor categories equipped with a neutral fiber functor (called Tannakian lattice), both defined over a Dedekind ring. We use ... WebIntroduction to Affine Group Schemes. Springer Science & Business Media, Nov 13, 1979 - Mathematics - 164 pages. Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take …
Flat affine group schemes
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WebIf we have an connected reductive group (reductive probably doesn't matter, affine group scheme is what matters) G Q over Q, we may construct a flat affine Z - group, such … WebNov 5, 2013 · Abstract: We establish a duality between flat affine group schemes and rigid tensor categories equipped with a neutral fiber functor (called Tannakian lattice), both …
WebThis is a modern exposition of the basic theory of affine group schemes. Although the emphasis is on affine group schemes of finite type over a field, we also discuss more … WebJul 14, 2024 · You found our list of the best group activities in Atlanta, Georgia. Fun group activities in Atlanta, GA, are events that get you and your team away from their work and …
WebNov 6, 2024 · The X -group scheme G is flat and affine. Yet the pushforward π ∗ G is a disjoint union of a copy of S and a copy of the open immersion j: V → S. This open immersion is not affine. If π: X → S is proper, flat and of finite presentation and W is an affine X -scheme, then π ∗ W → S is affine and of finite presentation. WebJan 23, 2024 · Abstract: We study affine group schemes over a discrete valuation ring $R$ using two techniques: Neron blowups and Tannakian categories. We employ the theory …
WebJul 1, 2024 · We establish some structural results for the Witt and Grothendieck--Witt groups of schemes over \Z [1/2], including homotopy invariance for Witt groups and a formula for the Witt and Grothendieck--Witt groups of punctured affine spaces over a scheme. All these results hold for singular schemes and at the level of spectra. Authors:
WebLet $S$ be a scheme. Let $(G, m)$ be a group scheme over $S$. We say $G$ is a smooth group scheme if the structure morphism $G \to S$ is smooth. We say $G$ is a flat … motor vehicle inspector syllabusWebApr 11, 2024 · ϕ: G × k G → G. is also a morphism of groups. What does "morphism of groups" means for schemes? For a Lie group G, it implies that the topological space has the structure of a group, i.e ϕ ( x y) = ϕ ( x) ϕ ( y) for all x, y ∈ G, etc. However, for schemes such a definition is confusing since we don't know what "type" of points such a ... healthy food for heart attack patientWebJames Milne -- Home Page healthy food for heartburnmotor vehicle inspector vacanciesWebA schemeis a locally ringed space Xadmitting a covering by open sets Ui, such that each Ui(as a locally ringed space) is an affine scheme.[8] In particular, Xcomes with a sheaf OX, which assigns to every open subset Ua commutative ring OX(U) called the … motor vehicle inspector booksWebMay 23, 2024 · To fix a context we consider ϕ: X → Y a morphism between two affine varieties over an algebraic closed field k. This give under the anti-equivalence of categories a k-algebra morphism ϕ ∗ between coordinate algebras of Y and X. However, ϕ ∗ injective doesn't imply ϕ surjective. motor vehicle inspector jobsAny affine group scheme is the spectrum of a commutative Hopf algebra (over a base S, this is given by the relative spectrum of an OS -algebra). The multiplication, unit, and inverse maps of the group scheme are given by the comultiplication, counit, and antipode structures in the Hopf … See more In mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all … See more • Given a group G, one can form the constant group scheme GS. As a scheme, it is a disjoint union of copies of S, and by choosing an identification of these copies with elements of G, … See more Suppose that G is a group scheme of finite type over a field k. Let G be the connected component of the identity, i.e., the maximal connected subgroup scheme. Then G is an … See more Cartier duality is a scheme-theoretic analogue of Pontryagin duality taking finite commutative group schemes to finite commutative group schemes. See more A group scheme is a group object in a category of schemes that has fiber products and some final object S. That is, it is an S-scheme G equipped with one of the equivalent sets of data • a triple of morphisms μ: G ×S G → G, e: S → G, and ι: G → … See more • The multiplicative group Gm has the punctured affine line as its underlying scheme, and as a functor, it sends an S-scheme T to the multiplicative group of invertible global … See more A group scheme G over a noetherian scheme S is finite and flat if and only if OG is a locally free OS-module of finite rank. The rank is a … See more healthy food for heart and lungs