相关论文: Variants of formal nearby cycles

We introduce a concept of formal local homology modules which is in some sense dual to P. Schenzel's concept of formal local cohomology modules. The dual theorem and the non-vanishing theorem of formal local homology modules will be shown.…

We prove a number of results on the \'etale cohomology of rigid analytic varieties over $p$-adic non-archimedean local fields. Among other things, we establish bounds for Frobenius eigenvalues, show a strong version of Grothendieck's local…

We make a systematic study of the infinitesimal lifting conditions of a pseudo finite type map of noetherian formal schemes. We recover the usual general properties in this context, and, more importantly, we uncover some new phenomena. We…

For a local system and a function on a smooth complex algebraic variety, we give a proof of a conjecture of M. Kontsevich on a formula for the vanishing cycles using the twisted de Rham complex of the formal microlocalization of the…

Recently, Chach\'olski, Neeman, Pitsch, and Scherer studied, in a series of three papers, model approximations for the unbounded category of cochain complexes over a commutative ring. These approximations allow to construct relative…

We develop a theory of nearby and vanishing cycles in the context of finite-coefficient Zariski-constructible sheaves over a non-archimedean field which is non-trivially valued, complete, algebraically closed, and of mixed characteristic or…

We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes…

Let $F$ be a field, let $D$ be a subring of $F$, and let ${\mathfrak{X}}$ be the Zariski-Riemann space of valuation rings containing $D$ and having quotient field $F$. We consider the Zariski, inverse and patch topologies on…

We study a notion of total acyclicity for complexes of flat sheaves over a scheme. It is Zariski-local - i.e. it can be verified on any open affine covering of the scheme - and it agrees, in their setting, with the notion studied by Murfet…

Let $\mathfrak a$ denote an ideal of a local ring $(R, \mathfrak m).$ Let $M$ be a finitely generated $R$-module. There is a systematic study of the formal cohomology modules $\varprojlim \HH^i(M/\mathfrak a^nM), i \in \mathbb Z.$ We…

We show that every scheme/algebraic space/stack that is quasi-compact with quasi-finite diagonal can be approximated by a noetherian scheme/algebraic space/stack. More generally, we show that any stack which is etale-locally a global…

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…

I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly…

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…

Let (R; m; k) be a local noetherian domain with field of fractions K and R_v a valuation ring, dominating R (not necessarily birationally). Let v|K be the restriction of v to K; by definition, v|K is centered at R. Let \hat{R} denote the…

This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…

In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the…

We are interested in classifying groups of local biholomorphisms (or even formal diffeomorphisms) that can be endowed with a canonical structure of algebraic group up to add extra formal diffeomorphisms. We show that this is the case for…

We study the notion of non-commumative higher dimensional local fields. A simplest example is the ring P of formal pseudo- differential operators. As an application we extend the KP hierarchy to the space $P^n$.

This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…