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.

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Special Year 2004-05: The Bloch-Kato Conjecture - Seminar

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 describe some bounds on the multidegrees of complete intersections to have trivial Chow groups in low dimensions.

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_...