相关论文: Rigidity of morphisms for log schemes

This thesis (defended 10/07/2019) develops a theory of networks of hybrid open systems and morphisms. It builds upon a framework of networks of continuous-time open systems as product and interconnection. We work out categorical notions for…

In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.

We establish rigidity (or uniqueness) theorems for nc automorphisms which are natural extensions of clasical results of H.~Cartan and are improvements of recent results. We apply our results to nc-domains consisting of unit balls of…

The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of…

In this paper, we discuss a rigidity property for holomorphic disks in Teichm\"uller space. In fact, we give a refinement of Tanigawa's rigidity theorem. We will also treat the rigidity property of holomorphic disks for complex manifolds.…

Using log-geometry, we construct a model for the configuration category of a smooth algebraic variety. As an application, we prove the formality of certain configuration spaces.

Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras.

In this paper, we prove compatibilities of various definitions of relatively unipotent log de Rham fundamental groups for certain proper log smooth integral morphisms of fine log schemes of characteristic zero. Our proofs are purely…

In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level.

This is a technical introduction to the paper "Extension of twisted Hodge metrics for Kahler morphisms" by the authors.

We construct the $\mathbb{A}^1$-local stable motivic homotopy categories of fs log schemes. For schemes with the trivial log structure, our construction is equivalent to the original construction of Morel-Voevodsky. We prove the…

Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Fefferman and Phong plays a central role in our analysis.

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.

In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…

The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups…

We show that any of a large class of schemes receives a universal homeomorphism from a reduced scheme that in turn receives no nontrivial universal homeomorphism from any other reduced scheme. This construction serves as a categorical input…

In this paper, we prove the termination of 4-fold semi-stable log flips under the assumption that there always exist 4-fold (semi-stable) log flips.

Assuming positive entropy we prove a measure rigidity theorem for higher rank actions on tori and solenoids by commuting automorphisms. We also apply this result to obtain a complete classification of disjointness and measurable factors for…