13 research outputs found
Deformation theory of objects in homotopy and derived categories III: abelian categories
This is the third paper in a series. In part I we developed a deformation
theory of objects in homotopy and derived categories of DG categories. Here we
show how this theory can be used to study deformations of objects in homotopy
and derived categories of abelian categories. Then we consider examples from
(noncommutative) algebraic geometry. In particular, we study noncommutative
Grassmanians that are true noncommutative moduli spaces of structure sheaves of
projective subspaces in projective spaces.Comment: Alexander Efimov is a new co-author of this paper. Besides some minor
changes, a new part (part 3) about noncommutative Grassmanians was adde
Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
This is the second paper in a series. In part I we developed deformation
theory of objects in homotopy and derived categories of DG categories. Here we
extend these (derived) deformation functors to an appropriate bicategory of
artinian DG algebras and prove that these extended functors are
pro-representable in a strong sense.Comment: Alexander Efimov is a new co-author of this paper. New material was
added: A_{\infty}-structures, Maurer-Cartan theory for A_{\infty}-algebras.
This allows us to strengthen our main results on the pro-representability of
pseudo-functors coDEF_{-} and DEF_{-}. We also obtain an equivalence between
homotopy and derived deformation functors under weaker hypothese
Deformation theory of objects in homotopy and derived categories I: general theory
This is the first paper in a series. We develop a general deformation theory
of objects in homotopy and derived categories of DG categories. Namely, for a
DG module over a DG category we define four deformation functors \Def
^{\h}(E), \coDef ^{\h}(E), \Def (E), \coDef (E). The first two functors
describe the deformations (and co-deformations) of in the homotopy
category, and the last two - in the derived category. We study their properties
and relations. These functors are defined on the category of artinian (not
necessarily commutative) DG algebras.Comment: Alexander Efimov is a new co-author of this paper. Besides some minor
changes, Proposition 7.1 and Theorem 8.1 were correcte
Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons
Measurements of the Collins and Sivers asymmetries for charged pions and charged and neutral kaons produced in semi-inclusive deep-inelastic scattering of high energy muons off transversely polarised protons are presented. The results were obtained using all the available COMPASS proton data, which were taken in the years 2007 and 2010. The Collins asymmetries exhibit in the valence region a non-zero signal for pions and there are hints of non-zero signal also for kaons. The Sivers asymmetries are found to be positive for positive pions and kaons and compatible with zero otherwise. © 2015