Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology class

关于Clemens-Schmid精确序列的处理

On the Clemens-Schmid exact sequence

本文从权重角度探讨了(Clemens-Schmid)精确序列，提出新的理论框架和方法，推动了代数几何领域的发展。

Clemens-Schmid exact sequence in characteristic p

For a semistable family of varieties over a curve in characteristic $p$, we prove the existence of a "Clemens-Schmid type" long exact sequence for the $p$-adic cohomology. The cohomology groups appearing in such a long exact sequence are defined locally

镜像 Clemens–Schmid 正合序列

The Mirror Clemens-Schmid Sequence

本文提出联系光滑簇与补开集上同调的四项长正合序列，证明其兼容反常 Leray 滤过和混合 Hodge 结构，并通过 K3、Calabi–Yau 及五次三维簇退化验证其为 Clemens–Schmid 序列的镜像。

Hodge theory of degenerations, (I): Consequences of the decomposition theorem

We use the Decomposition Theorem to derive several generalizations of the Clemens-Schmid sequence, relating asymptotic Hodge theory of a degeneration to the mixed Hodge theory of its singular fiber(s).

Degenerations and limit Frobenius structures in rigid cohomology

We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be effectively computable in an appropriate sense for a degeneration of projective hypersurfaces. We conjecture that the limiting Frobenius structure relates to the rigid cohomology of a semistable limit of the degeneration through an analogue of the Clemens-Schmidt exact sequence. Our construction is illustrated, and conjecture supported, by a selection of explicit ex…

通过节点退化对 K3 曲面 Hodge 猜想的构造性证明

Constructive Proof of the Hodge Conjecture for K3 Surfaces via Nodal Degenerations

本文提出不依赖 Torelli 定理的复 K3 曲面 Hodge 猜想构造性证明，借助至多十个 A_1-节点的四次退化、Clemens–Schmid 序列与 Picard–Lefschetz 理论，将任意有理 (1,1)-类实现为代数闭链。