Results 1  10
of
15
FORMAL LOOPS II: A LOCAL RIEMANNROCH THEOREM FOR DETERMINANTAL GERBES
, 2005
"... (0.1) The goal of this paper and the next one [KV2] is to relate three subjects of recent interest: (A) The theory of sheaves of chiral differential operators (CDO), see [GMS12]. A sheaf of CDO on a complex manifold X is a sheaf of graded vertex algebras with certain conditions on the graded compon ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(0.1) The goal of this paper and the next one [KV2] is to relate three subjects of recent interest: (A) The theory of sheaves of chiral differential operators (CDO), see [GMS12]. A sheaf of CDO on a complex manifold X is a sheaf of graded vertex algebras with certain conditions on the graded components. As shown in loc. cit., locally on X such an object always exists and is unique up to an isomorphism but the isomorphism not being canonical, the global situation is similar to the behavior of spinor bundles on a Riemannian manifold. This is expressed by saying that sheaves of CDO form a gerbe CDOX. A global object exists if and only if the characteristic class (0.1.1) ch2(X) = 1 2 c21 (X) − c2(X) vanishes. Manifolds with this property are known as MU〈8〉manifolds in homotopy theory. (B) The theory of the group GL(∞) developed by Sato and others [PS], in particular,
Φmodules and coefficient spaces
 Moscow Math. J
"... This paper is inspired by Kisin’s article [Ki1], in which he studies deformations of Galois representations of a local padic field which are defined by finite flat group schemes. The result of Kisin most relevant to our paper is his construction of a kind of resolution of the formal deformation spa ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
This paper is inspired by Kisin’s article [Ki1], in which he studies deformations of Galois representations of a local padic field which are defined by finite flat group schemes. The result of Kisin most relevant to our paper is his construction of a kind of resolution of the formal deformation space of the given Galois representation, by constructing a scheme which
Fourier transform and middle convolution for irregular Dmodules. arXiv:math/0808.0699
"... Abstract. In [3], S. Block and H. Esnault constructed the local Fourier transform for Dmodules. We present a different approach to the local Fourier transform, which makes its properties almost tautological. We apply the local Fourier transform to compute the local version of Katz’s middle convolut ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Abstract. In [3], S. Block and H. Esnault constructed the local Fourier transform for Dmodules. We present a different approach to the local Fourier transform, which makes its properties almost tautological. We apply the local Fourier transform to compute the local version of Katz’s middle convolution. 1.
TORIC ARC SCHEMES AND QUANTUM COHOMOLOGY OF TORIC VARIETIES.
, 2004
"... This paper is a part of a larger project devoted to the study of Floer cohomology in algebrogeometic context, as a natural cohomology theory defined on a certain class of indschemes. Among these indschemes are algebrogeometric models of the spaces of free loops. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper is a part of a larger project devoted to the study of Floer cohomology in algebrogeometic context, as a natural cohomology theory defined on a certain class of indschemes. Among these indschemes are algebrogeometric models of the spaces of free loops.
Formal loops III: Factorizing functions and the Radon transform
, 2005
"... 0. Introduction. (0.1) Let X be a C ∞manifold and η be a smooth 1form on X. Its Radon transform is the function τ(η) on the free loop space L(X) = C ∞ (S 1, X) whose value at γ: S1 → X is ∫ S1 γ∗η. This “universal ” setting includes many classical instances ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
0. Introduction. (0.1) Let X be a C ∞manifold and η be a smooth 1form on X. Its Radon transform is the function τ(η) on the free loop space L(X) = C ∞ (S 1, X) whose value at γ: S1 → X is ∫ S1 γ∗η. This “universal ” setting includes many classical instances
MITTAGLEFFLER CONDITIONS ON MODULES
, 704
"... Abstract. We study MittagLeffler conditions on modules providing relative versions of classical results by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we give a new argument for solving the Baer splitting problem. Moreover, we show that modules arising in ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. We study MittagLeffler conditions on modules providing relative versions of classical results by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we give a new argument for solving the Baer splitting problem. Moreover, we show that modules arising in cotorsion pairs satisfy certain MittagLeffler conditions. In particular, this implies that tilting modules satisfy a useful finiteness condition over their endomorphism ring. In the final section, we focus on a special tilting cotorsion pair related to the puresemisimplicity conjecture. Contents: 1. QMittagLeffler modules 5
GERBAL REPRESENTATIONS OF DOUBLE LOOP GROUPS
, 810
"... Abstract. A crucial role in representation theory of loop groups of reductive Lie groups and their Lie algebras is played by their nontrivial second cohomology classes which give rise to their central extensions (the affine Kac–Moody groups and Lie algebras). Loop groups embed into the group GL ∞ o ..."
Abstract
 Add to MetaCart
Abstract. A crucial role in representation theory of loop groups of reductive Lie groups and their Lie algebras is played by their nontrivial second cohomology classes which give rise to their central extensions (the affine Kac–Moody groups and Lie algebras). Loop groups embed into the group GL ∞ of continuous automorphisms of C((t)), and these classes come from a second cohomology class of GL∞. In a similar way, double loop groups embed into a group of automorphisms of C((t))((s)), denoted by GL∞,∞, which has a nontrivial third cohomology. In this paper we explain how to realize a third cohomology class in representation theory of a group: it naturally arises when we consider representations on categories rather than vector spaces. We call them “gerbal representations. ” We then construct a gerbal representation of GL∞, ∞ (and hence of double loop groups), realizing its nontrivial third cohomology class, on a category of modules over an infinitedimensional Clifford algebra. This is a twodimensional analogue of the fermionic Fock representations of the ordinary
EFACTORS FOR THE PERIOD DETERMINANTS OF CURVES
, 903
"... The myriad beings of the six worlds – gods, humans, beasts, ghosts, demons, and devils – are our relatives and friends. Tesshu “Bushido”, translated by J. Stevens. ..."
Abstract
 Add to MetaCart
The myriad beings of the six worlds – gods, humans, beasts, ghosts, demons, and devils – are our relatives and friends. Tesshu “Bushido”, translated by J. Stevens.