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Timetable (NSTW03)

K-theory and arithmetic

Sunday 29th September 2002 to Saturday 5th October 2002

Monday 30th September 2002
08:30 to 10:00 Registration
Session: K-theory and arithmetic
INI 1
10:00 to 11:00 A Scholl ([Cambridge])
Zeta elements and modular forms
Session: K-theory and arithmetic
shall explain the construction of `zeta elements' in K_k of Kuga-Sato varieties which form an Euler system, related via the dual exponential to critical L-values of weight k cusp forms, and via the regulator to non-critical values.
INI 1
11:00 to 11:30 Coffee
Session: K-theory and arithmetic
INI 1
11:30 to 12:30 S Bloch ([Chicago])
${\bf G}_{a}$, motives, polylogarithms etc
Session: K-theory and arithmetic
INI 1
12:30 to 13:30 Lunch at Wolfson Court
Session: K-theory and arithmetic
INI 1
14:00 to 15:00 C Soule (IHES)
Bounds on the torsion in the K-theory of algebraic integers
Session: K-theory 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: K-theory and arithmetic
INI 1
15:30 to 16:30 P Schneider ([Muenster])
Noncommutative Iwasawa Theory
Session: K-theory and arithmetic
INI 1
17:00 to 18:15 Welcome Wine Reception
Session: K-theory and arithmetic
INI 1
18:45 to 19:30 Dinner at Wolfson Court (Residents Only)
Session: K-theory and arithmetic
INI 1
Tuesday 1st October 2002
10:00 to 11:00 VP Snaith ([Southampton])
Stark's conjecture and new Stickelberger phenomena
Session: K-theory and arithmetic
INI 1
11:00 to 11:30 Coffee
Session: K-theory and arithmetic
INI 1
11:30 to 12:30 I Fesenko ([Nottingham])
Analysis on arithmetic surfaces
Session: K-theory and arithmetic
A new kind of measure matching properties of two-dimensional 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: K-theory and arithmetic
INI 1
14:00 to 15:00 Z Wojtkoviak ([Nice])
l-adic polylogarithms
Session: K-theory and arithmetic
INI 1
15:00 to 15:30 Tea
Session: K-theory and arithmetic
INI 1
15:30 to 16:30 C Pedrini ([Genova])
Finite-dimensional motives and the Beilinson-Bloch conjectures
Session: K-theory and arithmetic
INI 1
18:45 to 19:30 Dinner at Wolfson Court (Residents Only)
Session: K-theory and arithmetic
INI 1
Wednesday 2nd October 2002
10:00 to 11:00 M Taylor ([UMIST])
de Rham discriminants
Session: K-theory and arithmetic
INI 1
11:00 to 11:30 Coffee
Session: K-theory and arithmetic
INI 1
11:30 to 12:30 V Abrashkin ([Durham])
Analogue of the Grothendieck conjecture for higher dimensional local fields
Session: K-theory and arithmetic
INI 1
12:30 to 13:30 Lunch at Wolfson Court
Session: K-theory and arithmetic
INI 1
14:00 to 00:00 Free afternoon - sightseeing
Session: K-theory and arithmetic
INI 1
18:45 to 19:30 Dinner at Wolfson Court (Residents Only)
Session: K-theory and arithmetic
INI 1
Thursday 3rd October 2002
10:00 to 11:00 S Lichtenbaum ([Brown])
Weil \'{e}tale cohomology
Session: K-theory and arithmetic
INI 1
11:00 to 11:30 Coffee
Session: K-theory and arithmetic
INI 1
11:30 to 12:30 D Burns (King's College London)
On equivariant Tamagawa numbers, Weil \'{e}tale cohomology and values of L-functions
Session: K-theory and arithmetic
We show that, in certain cases, Lichtenbaum's Weil-Etale 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 L-functions.
INI 1
12:30 to 13:30 Lunch at Wolfson Court
Session: K-theory and arithmetic
INI 1
14:00 to 15:00 T Geisser ([USC])
Weil \'{e}tale motivic cohomology over finite fields
Session: K-theory and arithmetic
INI 1
15:00 to 15:30 Tea
Session: K-theory and arithmetic
INI 1
15:30 to 16:30 B Kahn ([Jussieu])
Rational and numerical equivalence on certain abelian varieties over finite fields
Session: K-theory and arithmetic
INI 1
20:00 to 00:00 Conference Dinner at Christ's College
Session: K-theory and arithmetic
INI 1
Friday 4th October 2002
10:00 to 11:00 U Jannsen ([Regensburgh])
Kato complexes: conjectures and results
Session: K-theory and arithmetic
For rather general schemes Kato defined complexes which are Galois cohomology analogues of the Gersten complexes in K-theory (Crelle 366: `A Hasse principle for 2-dimensional 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: K-theory and arithmetic
INI 1
11:30 to 12:30 A Schmidt ([Heidelberg])
Relative K-groups and class field theory of arithmetic surfaces
Session: K-theory and arithmetic
INI 1
12:30 to 13:30 Lunch at Wolfson Court
Session: K-theory and arithmetic
INI 1
14:00 to 15:00 R De Jeu ([Durham])
$K_{4}$ of curves and syntomic regulators
Session: K-theory and arithmetic
INI 1
15:00 to 15:30 Tea
Session: K-theory and arithmetic
INI 1
15:30 to 16:30 W Gajda ([UAM])
K-theory and classical conjectures in the arithmetic of cyclotomic fields
Session: K-theory and arithmetic
INI 1
18:45 to 19:30 Dinner at Wolfson Court (Residents Only)
Session: K-theory and arithmetic
INI 1
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons