可对角化\(p\)-群的作用与模\(p\)陈数

Chern numbers for singular varieties and elliptic homology

A fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones. Intersection homology, for example, directly produces groups associated to any variety which have almost all the properties of the usual homology groups of a smooth variety. Minimal model theory suggests the possibility of working more indirectly by relating any singular variety to a variety which is smooth or nearly so. Here we use ideas from minimal model theory to define some characteristic numbers for singular varieties, generalizing the Chern numbers of a smooth variety. This was s…

Representation theory and the cycle map of a classifying space

We compute the Chern subgroup of the 4-th integral cohomology group of a certain classifying space and show that it is a proper subgroup. Such a classifying space gives us new counterexamples for the integral Hodge and Tate conjectures modulo torsion.

Metastable complex vector bundles over complex projective spaces

We apply Weiss calculus to compute the number of topological complex vector bundles of rank $n-2$ with vanishing Chern classes over $\mathbb{C}P^n$ for $n>3$, as given by the list $1, 1, 12, 2, 1, 3, 2, 2, 3, 1, 4, 6, 1, 1, 6, 2, 1, 3, 4, 2, 3, 1, 2, 6$, where the $i$-th entry in this list is the number of such bundles whenever $n$ is congruent to $i$ modulo $24$, starting with $i = 0$. Similarly, the number of rank $n-1$ bundles with vanishing Chern classes over $\mathbb{C}P^n$ for $n>2$ is $2$ when $n$ is odd and $1$ when $n$ is even.

Numerical equivalence defined on Chow groups of Noetherian local rings

In the present paper, we define a notion of numerical equivalence on Chow groups or Grothendieck groups of Noetherian local rings, which is an analogue of that on smooth projective varieties. Under a mild condition, it is proved that the Chow group modulo numerical equivalence is a finite dimensional ${\Bbb Q}$-vector space, as in the case of smooth projective varieties. Numerical equivalence on local rings is deeply related to that on smooth projective varieties. For example, if Grothendieck's standard conjectures are true, then a vanishing of Chow group (of local rings) modulo numerical equi…

Komplexe elliptische Geschlechter und S^1-aequivariante Kobordismustheorie（复椭圆亏格与S^1-等变配边理论）

Komplexe elliptische Geschlechter und S^1-aequivariante Kobordismustheorie (Complex elliptic genera and S^1-equivariant cobordism theory)

本文引入万有复椭圆亏格并证明其S^1-作用刚性，刻画其核，构造基序列，并证明Level N亏格在特定余维数爆破下的不变性。