Related papers: A Frobenius theorem in algebraic geometry

To any finite local embedding of Deligne--Mumford stacks $g: Y\to X$ we associate an \'etale, universally closed morphism $F_{Y/X}\to X$ such that for the complement $Y^2_X$ of the image of the diagonal $Y \to Y\times_XY$, the stack…

We generalize the notion of expanded degenerations and pairs for a simple degeneration or smooth pair to the case of smooth Deligne-Mumford stacks. We then define stable quotients on the classifying stacks of expanded degenerations and…

We formulate and prove a non-abelian analog of Deligne's Fixed Part theorem on Hodge classes, revisiting previous work of Jost--Zuo, Katzarkov--Pantev and Landesman--Litt. To this aim we study algebraically isomonodromic extensions of local…

This paper describes how, in the case of algebraic surfaces, the well-known theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized 'multiplier ideal sheaves', following the ideas of Siu. The key concept is that the…

We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…

We identify a class of singular algebraic foliations whose leaves through singular points retain regularity. The proof consists in showing existence of residual gerbes for certain formal stacks, which do not enjoy smooth presentations. As…

We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the…

Kazhdan and Lusztig identified the affine Hecke algebra $\mathcal{H}$ with an equivariant $K$-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of…

We study how to use a suitably ample locally free sheaf over a proper Deligne-Mumford stack to furnish an embedding of the stack into a geometric invariant theory (GIT) quotient stack constructed from a finite-dimensional linear…

Starting from the problem of describing cohomological invariants of Poisson manifolds we prove in a sense a ``no-go'' result: the differential graded Lie algebra of de Rham forms on a smooth Poisson manifold is formal.

We prove the formality theorem for the differential graded Lie algebra module of Hochschild chains for the algebra of endomorphisms of a smooth vector bundle. We discuss a possible application of this result to a version of the algebraic…

We define and study certain moduli stacks of modules equipped with a Frobenius semi-linear endomorphism. These stacks can be thought of as parametrizing the coefficients of a variable Galois representation and are global variants of the…

In this paper, we construct in characteristic zero a derived foliation on derived mapping stacks $\underline{\mathbf{Map}}_S(X,Y)$, for $S$ a base derived stack, $X$ a proper schematic, flat, and local complete intersection derived stack…

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $[M/G]$, where $M$ is a smooth manifold equipped with a smooth proper action by a Lie group $G$.…

This thesis is concerned with equidistant foliations of Euclidean space, i.e. partitions into complete, connected, properly embedded smooth submanifolds. The space of leaves is an Alexandrov space of nonnegative curvature and the canonical…

We give conditions for a n-connective quasicoherent obstruction theory on a Deligne-Mumford stack to come from the structure of a connective spectral Deligne-Mumford stack on the underlying topos.

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds,…

In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…

We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the DG algebra RHom(F,F) is formal for any sheaf F polystable with respect to an ample line bundle. Our main tool is the uniqueness of DG…

Relations between some kinds of formal and standard smoothness, for morphisms of schemes, are clarified in surprisingly simple and direct ways, bypassing much of the customarily employed machinery. Even the deep local-to-global property of…