Previous Special Year Seminar
Bass' NK Groups and cdh-Fibrant Hochschild Homology
By definition, NK_0(R) is K_0(R[t]) modulo K_0(R). We give a
formula for this group when R is of finite type over a field of
characteristic zero. The group is bigraded and determined by its
typical pieces, which are the cdh cohomology groups H^p(R...
Arithmetic Cohomology and Special Values of Zeta-Functions (after Geisser)
Geisser gives conjectured formulas for special values of
zeta-functions of varieties over finite fields in terms of Euler
characteristics of arithmetic cohomology (an improved version of
Weil-etale cohomology). He then proves these formulas under...
The Syntomic Regulator for K_1 of Surfaces
We give an explicit formula for the syntomic regulator of
certain elements in the first algebraic K-theory group of a smooth
complete surface over the ring of integers of a p-adic field. The
formula uses the theory of Coleman integration and the...
An Approach to the Conservation of the Nearby Motive Functor
We present a program to prove the following conjecture: Let $S$
be the spectrum of a DVR of equi-characteristic zero with field of
fraction $K$ and residue field $k$. The functor (associated to the
choice of a uniformizing) $\Psi:DM_{gm}(K) \to DM_...
Finite Generation VI: Moduli Spaces
We will finish the sketch of the proof of existence of a
geometrically meaningful compactification of the moduli space of
canonically polarized smooth varieties.
Rost's Basic Corespondences
Parabolic Chern Character of the de Rham Bundles
Characteristic classes of Flat bundles on smooth algebraic
varieties are defined in various cohomology theories. We consider
the de Rham cohomology, the Deligne cohomology and the rational
Chow groups and study the classes. We focus on the special...
Witten Equation and Singularity Theory
Yongbin Ruan
In 1991, Witten proposed a famous conjecture (solved by
Kontsevich) related the intersection theory of Deligne-Mumford
moduli space to KDV-integrable hierearchy. To generalize his
conjecture, Witten proposed a remarkable PDE based any...
Using Rost Motives to Prove Bloch-Kato
Moduli Spaces via Minimal Models (cont'd)
