5 papers · 1 filter
Infinitesimally Equivariant Bundles on Complex Manifolds
Emile Bouaziz
We show that any continuous -linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential…
Annihilators of -modules and differential operators
Emile Bouaziz, Henrique Rocha
For a smooth algebraic variety , we study the category of finitely generated modules over the ring of function of that has a compatible action of the Lie algebra $\mathcal{V…
Non-Archimedean Fréchet Algebras and the Loop Space of a Hypersurface Complement
Emile Bouaziz
We study the space of loops into a hypersurface complement, and show that the corresponding topological algebra of Laurent series with coefficients in $\mathcal{O}(L\mathbf{A}^{d}_…
Derived Geometry and Non-Linear Differential Equations on the Punctured Disc
Emile Bouaziz
We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to…
Topology of Singularities on Algebraic Loop Spaces
Emile Bouaziz
We study the topology of some simple infinite dimensional singularities arising from spaces of \emph{algebraic formal loops}. We prove that in some simple cases the natural analogu…