Results 1  10
of
46
Homotopical algebraic geometry. II. Geometric stacks and applications
, 2006
"... ..."
(Show Context)
Derived Quot schemes
"... (0.1) A typical moduli problem in geometry is to construct a “space ” H parametrizing, up to isomorphism, objects of some given category Z (e.g., manifolds, vector bundles etc.). This can be seen as a kind of a nonAbelian cohomology problem and the construction usually consists of two steps of oppo ..."
Abstract

Cited by 44 (1 self)
 Add to MetaCart
(Show Context)
(0.1) A typical moduli problem in geometry is to construct a “space ” H parametrizing, up to isomorphism, objects of some given category Z (e.g., manifolds, vector bundles etc.). This can be seen as a kind of a nonAbelian cohomology problem and the construction usually consists of two steps of opposite nature, namely applying
Modules and Morita theorem for operads
 Am. J. of Math
"... (0.1) Morita theory. Let A, B be two commutative rings. If their respective categories of modules are equivalent, then A and B are isomorphic. This is not anymore true if A and/or B are not assumed to be commutative. Morita theory ..."
Abstract

Cited by 38 (0 self)
 Add to MetaCart
(Show Context)
(0.1) Morita theory. Let A, B be two commutative rings. If their respective categories of modules are equivalent, then A and B are isomorphic. This is not anymore true if A and/or B are not assumed to be commutative. Morita theory
Moduli Spaces of Commutative Ring Spectra
, 2003
"... Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E#E is flat over E# . We wish to address the following question: given a commutative E# algebra A in E#Ecomodules, is there an E# ring spectrum X with E#X = A as comodule algebras? We will formulate this as ..."
Abstract

Cited by 33 (0 self)
 Add to MetaCart
(Show Context)
Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E#E is flat over E# . We wish to address the following question: given a commutative E# algebra A in E#Ecomodules, is there an E# ring spectrum X with E#X = A as comodule algebras? We will formulate this as a moduli problem, and give a way  suggested by work of Dwyer, Kan, and Stover  of dissecting the resulting moduli space as a tower with layers governed by appropriate AndreQuillen cohomology groups. A special case is A = E#E itself. The final section applies this to discuss the LubinTate or Morava spectra En .
Derived Hilbert schemes
 J. A.M.S
"... (0.1) The Derived Deformation Theory (DDT) program (see [Kon], [CK] for more details and historical references) seeks to avoid the difficulties related to the singular nature of the moduli spaces in geometry by “passing to the derived category”, i.e., developing an appropriate version of the (nonabe ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
(Show Context)
(0.1) The Derived Deformation Theory (DDT) program (see [Kon], [CK] for more details and historical references) seeks to avoid the difficulties related to the singular nature of the moduli spaces in geometry by “passing to the derived category”, i.e., developing an appropriate version of the (nonabelian) derived functor of the functor
Moduli problems for structured ring spectra
 DANIEL DUGGER AND BROOKE
, 2005
"... In this document we make good on all the assertions we made in the previous paper “Moduli spaces of commutative ring spectra ” [20] wherein we laid out a theory a moduli spaces and problems for the existence and uniqueness of E∞ring spectra. In that paper, we discussed the the HopkinsMiller theore ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
In this document we make good on all the assertions we made in the previous paper “Moduli spaces of commutative ring spectra ” [20] wherein we laid out a theory a moduli spaces and problems for the existence and uniqueness of E∞ring spectra. In that paper, we discussed the the HopkinsMiller theorem on the LubinTate or Morava spectra En; in particular, we showed how to prove that the moduli space of all E ∞ ring spectra X so that (En)∗X ∼ = (En)∗En as commutative (En) ∗ algebras had the homotopy type of BG, where G was an appropriate variant of the Morava stabilizer group. This is but one point of view on these results, and the reader should also consult [3], [38], and [41], among others. A point worth reiterating is that the moduli problems here begin with algebra: we have a homology theory E ∗ and a commutative ring A in E∗E comodules and we wish to discuss the homotopy type of the space T M(A) of all E∞ring spectra so that E∗X ∼ = A. We do not, a priori, assume that T M(A) is nonempty, or even that there is a spectrum X so that E∗X ∼ = A as comodules.
Homotopy theory of modules over operads and nonΣ operads in monoidal model categories
 J. Pure Appl. Algebra
"... There are many interesting situations in which algebraic structure can be described ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
(Show Context)
There are many interesting situations in which algebraic structure can be described
Every homotopy theory of simplicial algebras admits a proper model
 Topology Appl. 119
, 2002
"... Abstract. We show that any closed model category of simplicial algebras over an algebraic theory ..."
Abstract

Cited by 18 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We show that any closed model category of simplicial algebras over an algebraic theory
Configuration spaces with summable labels
 Proceedings of BCAT98
"... Let M be an nmanifold, and let A be a space with a partial sum behaving as an nfold loop sum. We define the space C(M; A) of configurations in M with summable labels in A via operad theory. Some examples are symmetric products, labelled configuration spaces, and spaces of rational curves. We show ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
(Show Context)
Let M be an nmanifold, and let A be a space with a partial sum behaving as an nfold loop sum. We define the space C(M; A) of configurations in M with summable labels in A via operad theory. Some examples are symmetric products, labelled configuration spaces, and spaces of rational curves. We show that C(I n, ∂I n; A) is an nfold classifying space of C(I n; A), and for n = 1 it is homeomorphic to the classifying space by Stasheff. If M is compact, parallelizable, and A is path connected, then C(M; A) is homotopic to the mapping space Map(M, C(I n, ∂I n; A)).