arXiv subjects

Ting Li

Publications and source records attributed to Ting Li.

166 records · Page 10Linked to original sources

arXiv2010

The $\ell$-adic Dualizing Complex on an Excellent Surface with Rational Singularities

In this article, we show that if $X$ is an excellent surface with rational singularities, the constant sheaf $\mathbb{Q}_{\ell}$ is a dualizing complex. In coefficient $\mathbb{Z}_{\ell}$, we also prove that the obstruction for $\mathbb{Z}_{\ell}$ to become a dualizing complex lying on the divisor class groups at singular points. As applications, we study the perverse sheaves and the weights of $\ell$-adic cohomology groups on such surfaces.

math.AG↗

arXiv2008

The Étale Homology and The Cycle Maps in Adic Coefficients

In this article, we define the l-adic homology for a morphism of schemes satisfying certain finiteness conditions. This homology has these functors similar to the Chow groups: proper push-forward, flat pull-back, base change, cap-product, etc. In particular on singular varieties, this kind of l-adic homology behaves much better that the classical l-adic cohomology. As an application, we give an much easier approach to construct the cycle maps for arbitrary algebraic schemes over fields of finite cohomology dimension. And we prove these cycle maps kill the algebraic equivalences and commute with the Chern action of locally free sheaves.

math.AG↗

arXiv2007

Purely Algebraic Method to Construct Toric Schemes

In this article, we first give some elementary proprieties of monoids and fans, then construct a toric scheme over an arbitrary ring, from a given fan. Using Valuative Criterion, we prove that this scheme is separated and give the sufficient and necessary condition when it is proper. We also study the regularity and logarithmic regularity of it. Finally we study the morphisms of toric schemes induced by the homomorphisms of fans.

math.AG↗

arXiv2007

Log Structures on Generalized Semi-Stable Varieties

This is my PhD Thesis, part of it has published in Acta Mathematica Sinica. In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called semi-stable log structures exists if and only if the obstruction vanishes. In the case of no power, if the obstruction vanishes, then the semi-stable log structure is unique up to a unique isomorphism. So we obtain a kind of canonical structures on this family of morphisms.

math.AG↗