Related papers: Infinitesimal local study of formal schemes

Let (A,m_A) -> (B,m_B) be a local morphism of local noetherian rings and M a finitely generated B-module. Then it follows from Tor^A_1(M,A/m_A) = 0 that M is a flat A-module. This is usually called the "local criterion of flatness". We give…

The generalisation of the well-known (Hilbert polynomial) criterion for flatness of a projective morphism of Noetherian schemes is given for the case of nonreduced base of the morphism.

The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the…

We define the notion of a specialization morphism from a locally noetherian analytic adic space to a scheme. This captures the (classical) specialization morphism associated to a formal scheme. There is a well behaved theory of…

Grothendieck duality theory assigns to essentially-finite-type maps f of noetherian schemes a pseudofunctor f^\times right-adjoint to Rf_*, and a pseudofunctor f^! agreeing with f^\times when f is proper, but equal to the usual inverse…

Let S be a Noetherian scheme, f:X->Y a surjective S-morphism of S-schemes, with X of finite type over S. We discuss what makes Y of finite type. First, we prove that if S is excellent, Y is reduced, and f is universally open, then Y is of…

We prove that a Noetherian ring $R$ is a splinter if and only if for every equidimensional surjective morphism $\operatorname{Spec}(S) \to \operatorname{Spec}(R)$, the map $R \to S$ is pure. This yields a large, nontrivial class of ring…

We investigate flat maps where the source or target is a Noetherian ring, giving necessary and/or sufficient conditions on a ring for such maps to exist. Along the way, we develop some general facts about flat ring maps, and exhibit many…

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 three previous papers, we introduce the notion of formal manifolds and study…

We classify the invariant Borel measures for adic transformations, where the alphabets have bounded size and the measure is finite on the path space of some sub-Bratteli diagram. We develop a nonstationary version of the Frobenius normal…

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…

Let $X$ be a normal noetherian scheme and $Z \subseteq X$ a closed subset of codimension $\geq 2$. We consider here the local obstructions to the map $\hat{\pi}_{1}(X\backslash Z) \to \hat{\pi}_{1}(X)$ being an isomorphism. Assuming $X$ has…

A noetherian form is an abstract self-dual framework suitable for establishing homomorphism theorems (such as the isomorphism theorems and homological diagram lemmas) for group-like structures. In this paper we identify and carry out an…

Let $f$ be a holomorphic mapping between compact complex manifolds. We give a criterion for $f$ to have {\it unobstructed deformations}, i.e. for the local moduli space of $f$ to be smooth: this says, roughly speaking, that the group of…

We construct a 2-category of differential graded schemes. The local affine models in this theory are differential graded algebras, which are graded commutative with unit over a field of characteristic zero, are concentrated in non-positive…

In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we…

Smooth manifolds have been always understood intuitively as spaces with an affine geometry on the infinitesimal scale. In Synthetic Differential Geometry this can be made precise by showing that a smooth manifold carries a natural structure…

In this article we give a sufficient condition for a morphism $\varphi$ from a smooth variety $X$ to projective space, finite onto a smooth image, to be deformed to an embedding. This result puts some theorems on deformation of morphisms of…

Our main result establishes functorial desingularization of noetherian quasi-excellent schemes over $\bfQ$ with ordered boundaries. A functorial embedded desingularization of quasi-excellent schemes of characteristic zero is deduced.…