Algebraic foliations and derived geometry: the Riemann–Hilbert correspondence

On the k-nullity foliations in Finsler geometry

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

Noncommutative Geometry of Foliations

We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.

Derived Algebraic Geometry V: Structured Spaces

1 Structure Sheaves 7 1.1 C-Valued Sheaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 The Factorization System on StrG(X) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4 Classifying ∞-Topoi . . . . . . . . . . . . ....

Derived Algebraic Geometry VII: Spectral Schemes

Derived Algebraic Geometry III: Commutative Algebra

1 ∞-Operads 4 1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Fibrations of ∞-Operads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Algebra Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Cartesian Monoidal Structures . . . . . . . . . . ....