Previous Special Year Seminar
Abelian Relations on Webs and Abelian Families of 0-Cycles
Completion of the Proof of the Bloch-Kato Conjecture
Chuck Weibel
In the last eight lectures, we have reduced the proof of the
Bloch-Kato to an assertion about motivic cohomology operations. We
will prove that this assertion is correct, and so complete the
proof of the Bloch-Kato conjecture.
Overconvergent Homotopy Invariant Presheaves with Transfers over Smooth Rigid Varieties
Let F be a presheaf with transfers on the category of smooth
affinoid varieties over a non-archemidean field. Suppose that F is
overconvergent and homotopy invariant. Then the presheaves H^i(-,F)
are also homotopy invariant (where the cohomology is...
Wonderful Compactification of an Arrangement of Subvarieties
Li Li
Consider an arrangement of nonsingular subvarieties in a
nonsingular algebraic variety. We define a compactification of the
complement by replacing these subvarieties with a normal crossing
divisor. This compactification is obtained by a sequence of...
Cycles on Complete Intersections
We will describe some bounds on the multidegrees of complete
intersections to have trivial Chow groups in low dimensions.
On the Abel-Radon Transform of Locally Residual Currents with Respect to a Family of Complete Intersections
Let $X\subset \P^N$ be a projective submanifold of dimension $n$
in the complex projective space $\P^N$. Let $U$ be a domain in the
parameter space $T$ of complete intersections of codimension $m$
and of a given bidegree $(d_1,\dots,d_m)$ in $\P^N$...
Operations with Integer Coefficients (After Voevodsky)
We will classify all unstable motivic operations from bidegree
(2n,n) (with coefficients Z) to bidegree (p,q) with coefficients
Z/l, l>2. All such operations are polynomials on the elements of
the Steenrod Algebra. This work is based upon some...
Canonical Frames for Nonholonomic Vector Distributions
Igor Zelenko
The talk is based on the joint work with Boris Doubrov. First we
will describe a new rather effective procedure of symplectification
for the problem of local equivalence of nonholonomic vector
distributions. The starting point of this procedure is...
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...
