arXiv subjects
Publications and source records attributed to E. Bouaziz.
In their work, \cite{GR}, Gaitsgory and Rozenblyum introduce a derived version of the well-studied arc spaces of classical algebraic geometry. They observe that these derived spaces do not differ from their classical counterparts in the case of smooth schemes. In this note we will see that this is also the case for reduced local complete intersection schemes
We construct and study some vertex theoretic invariants associated to Poisson varieties, specialising in the conformal weight $0$ case to the familiar package of Poisson homology and cohomology. In order to do this conceptually we sketch a version of the \emph{calculus}, in the sense of \cite{TT}, adapted to the context of vertex algebras. We obtain the standard theorems of Poisson (co)homology in this \emph{chiral} context. This is part of a larger project related to promoting non-commutative geometric structures to chiral versions of such.
We study natural D-modules on the moduli stack of elliptic curves over a field of characteristic zero. We use this to produce an algebro-geometric version of the algebra of higher depth mock modular forms, studied from a Conformal Field Theoretic perspective by numerous authors.
We study some semi-infinite invariants associated to Landau-Ginzburg models. These specialize classically to the usual twisted de Rham package and in the case of vanishing potential to the chiral de Rham complex of Malikov, Schechtman and Vaintrob, \cite{MSV}. Further we offer some small evidence that these semi-infinite invariants can be associated to dg- categories more generally, so that in the classical limit they reproduce the usual non-commutative Hodge theory associated to the category.
We study the topology of the complex points of the algebraic loop space of a smooth curve.
We give a local model for d-shifted symplectic dg-schemes, or Deligne-Mumford dg-stacks [PTVV]. Locally any such is a product of a "twisted shifted cotangent bundle", where the twist is given by an element df, with $f \in H^{1-d}(\Cal O)$, and a quadratic bundle in middle degree. The latter only occurs if d = 4r+2.