Ktheory and arithmetic
Sunday 29th September 2002 to Saturday 5th October 2002
08:30 to 10:00 
Registration Session: Ktheory and arithmetic 
INI 1 
10:00 to 11:00 
Zeta elements and modular forms Session: Ktheory and arithmetic
shall explain the construction of `zeta elements' in K_k of KugaSato varieties which form an Euler system, related via the dual exponential to critical
Lvalues of weight k cusp forms, and via the regulator to noncritical
values.

INI 1 
11:00 to 11:30 
Coffee Session: Ktheory and arithmetic 
INI 1 
11:30 to 12:30 
${\bf G}_{a}$, motives, polylogarithms etc Session: Ktheory and arithmetic 
INI 1 
12:30 to 13:30 
Lunch at Wolfson Court Session: Ktheory and arithmetic 
INI 1 
14:00 to 15:00 
C Soule (IHES) Bounds on the torsion in the Ktheory of algebraic integers Session: Ktheory and arithmetic
Given a natural integer $m$ and a number field $F$ we find an
upper bound for the cardinality of the torsion in $K_{m}(A)$,
where $A$ is the ring of integers of $F$. The bound depends on $m$, the
absolute degree of $F$ and its absolute discriminant. This bound seems
much too big but it is explicit.

INI 1 
15:00 to 15:30 
Tea Session: Ktheory and arithmetic 
INI 1 
15:30 to 16:30 
Noncommutative Iwasawa Theory Session: Ktheory and arithmetic 
INI 1 
17:00 to 18:15 
Welcome Wine Reception Session: Ktheory and arithmetic 
INI 1 
18:45 to 19:30 
Dinner at Wolfson Court (Residents Only) Session: Ktheory and arithmetic 
INI 1 
10:00 to 11:00 
Stark's conjecture and new Stickelberger phenomena Session: Ktheory and arithmetic 
INI 1 
11:00 to 11:30 
Coffee Session: Ktheory and arithmetic 
INI 1 
11:30 to 12:30 
I Fesenko ([Nottingham]) Analysis on arithmetic surfaces Session: Ktheory and arithmetic
A new kind of measure matching properties of twodimensional structures on arithmetic surfaces is used to define zeta integrals on $K$delic groups and to study its properties.

INI 1 
12:30 to 13:30 
Lunch at Wolfson Court Session: Ktheory and arithmetic 
INI 1 
14:00 to 15:00 
Z Wojtkoviak ([Nice]) ladic polylogarithms Session: Ktheory and arithmetic 
INI 1 
15:00 to 15:30 
Tea Session: Ktheory and arithmetic 
INI 1 
15:30 to 16:30 
C Pedrini ([Genova]) Finitedimensional motives and the BeilinsonBloch conjectures Session: Ktheory and arithmetic 
INI 1 
18:45 to 19:30 
Dinner at Wolfson Court (Residents Only) Session: Ktheory and arithmetic 
INI 1 
10:00 to 11:00 
de Rham discriminants Session: Ktheory and arithmetic 
INI 1 
11:00 to 11:30 
Coffee Session: Ktheory and arithmetic 
INI 1 
11:30 to 12:30 
Analogue of the Grothendieck conjecture for higher dimensional local fields Session: Ktheory and arithmetic 
INI 1 
12:30 to 13:30 
Lunch at Wolfson Court Session: Ktheory and arithmetic 
INI 1 
14:00 to 00:00 
Free afternoon  sightseeing Session: Ktheory and arithmetic 
INI 1 
18:45 to 19:30 
Dinner at Wolfson Court (Residents Only) Session: Ktheory and arithmetic 
INI 1 
10:00 to 11:00 
S Lichtenbaum ([Brown]) Weil \'{e}tale cohomology Session: Ktheory and arithmetic 
INI 1 
11:00 to 11:30 
Coffee Session: Ktheory and arithmetic 
INI 1 
11:30 to 12:30 
On equivariant Tamagawa numbers, Weil \'{e}tale cohomology and values of Lfunctions Session: Ktheory and arithmetic
We show that, in certain cases, Lichtenbaum's WeilEtale cohomology leads to a more explicit interpretation of the (equivariant) Tamagawa number conjecture. We then use this interpretation to formulate, and in certain cases also prove, a universal refinement of the well known (and seemingly rather different) conjectures of Stark, of Gross, of Tate,
of Rubin and of Darmon concerning the values of derivatives of abelian
Lfunctions.

INI 1 
12:30 to 13:30 
Lunch at Wolfson Court Session: Ktheory and arithmetic 
INI 1 
14:00 to 15:00 
Weil \'{e}tale motivic cohomology over finite fields Session: Ktheory and arithmetic 
INI 1 
15:00 to 15:30 
Tea Session: Ktheory and arithmetic 
INI 1 
15:30 to 16:30 
Rational and numerical equivalence on certain abelian varieties over finite fields Session: Ktheory and arithmetic 
INI 1 
20:00 to 00:00 
Conference Dinner at Christ's College Session: Ktheory and arithmetic 
INI 1 
10:00 to 11:00 
U Jannsen ([Regensburgh]) Kato complexes: conjectures and results Session: Ktheory and arithmetic
For rather general schemes Kato defined complexes which are Galois cohomology analogues of the Gersten complexes in Ktheory (Crelle 366: `A Hasse principle for 2dimensional local fields'). He stated some conjectures and proved them in low dimensions. I will report on the results known so far (partly due to myself) and some relationships with étale dulaity (recent joint work with Saito and Sato).

INI 1 
11:00 to 11:30 
Coffee Session: Ktheory and arithmetic 
INI 1 
11:30 to 12:30 
Relative Kgroups and class field theory of arithmetic surfaces Session: Ktheory and arithmetic 
INI 1 
12:30 to 13:30 
Lunch at Wolfson Court Session: Ktheory and arithmetic 
INI 1 
14:00 to 15:00 
$K_{4}$ of curves and syntomic regulators Session: Ktheory and arithmetic 
INI 1 
15:00 to 15:30 
Tea Session: Ktheory and arithmetic 
INI 1 
15:30 to 16:30 
Ktheory and classical conjectures in the arithmetic of cyclotomic fields Session: Ktheory and arithmetic 
INI 1 
18:45 to 19:30 
Dinner at Wolfson Court (Residents Only) Session: Ktheory and arithmetic 
INI 1 