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.
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...
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...
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...
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...
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...
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_...
