Quotients of Algebraic Groups
نویسنده
چکیده
In this note, we study the existence and structure of the homogeneous space G/H for algebraic groups H ⊂ G. Let k be a field. All schemes considered will be k-schemes. By an affine algebraic group, we mean an affine group scheme of finite type over k. Note that we do not assume our schemes are reduced yet. We will only consider affine algebraic groups. From now on, G will denote an algebraic group unless otherwise stated.
منابع مشابه
IDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTS
In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.
متن کاملQuotients by non-reductive algebraic group actions
Geometric invariant theory (GIT) was developed in the 1960s by Mumford in order to construct quotients of reductive group actions on algebraic varieties and hence to construct and study a number of moduli spaces, including, for example, moduli spaces of bundles over a nonsingular projective curve [26, 28]. Moduli spaces often arise naturally as quotients of varieties by algebraic group actions,...
متن کاملA classification of hull operators in archimedean lattice-ordered groups with unit
The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...
متن کاملNonabelian Localization in Equivariant K-theory and Riemann-roch for Quotients
We prove a localization formula in equivariant algebraic K-theory for an arbitrary complex algebraic group acting with finite stabilizer on a smooth algebraic space. This extends to non-diagonalizable groups the localization formulas of H.A. Nielsen [Nie] and R. Thomason [Tho5] As an application we give a Riemann-Roch formula for quotients of smooth algebraic spaces by proper group actions. Thi...
متن کاملOn Quotient Stacks
A natural problem in algebraic geometry is the formation of quotients. This is particularly important in the theory of moduli, where many moduli spaces are naturally constructed as quotients of parameter spaces by linear algebraic groups. Examples of quotient moduli spaces include moduli spaces of curves, stable maps and stable vector bundles (with fixed determinant). Unfortunately, the quotien...
متن کاملSymplectic implosion and non-reductive quotients
There is a close relationship between Mumford’s geometric invariant theory (GIT) in (complex) algebraic geometry and the process of reduction in symplectic geometry. GIT was developed to construct quotients of algebraic varieties by reductive group actions and thus to construct and study moduli spaces [28, 29]. When a moduli space (or a compactification of a moduli space) over C can be construc...
متن کامل