#### A Newton Institute Workshop

#### During the programme on Arithmetic
Geometry (organizers J-L Colliot-Thélène, J Nekovár,
C Soulé)

at the Newton Institute (Cambridge, UK),

### Arakelov Theory, Values of L-Functions

#### 29 June to 3 July 1998

*Organizers: J Nekovár and C Soulé*

### Monday 29 June

09.00-11.00 Registration

11.00-11.30 Coffee

11.30-12.30 A Goncharov (Brown)

*Multiple $\zeta$-values and modular complexes *

13.00-14.00 Lunch

14.00-15.30 Pilgrimage to the bank

15.30-16.30 P Vojta (Berkeley)

*On Bu"chi's problem and Hilbert's tenth problem *

16.30-17.00 Tea

17.00-18.00 KI Yoshikawa (Nagoya)

*Analytic torsion and automorphic forms on the moduli space *

18.00-19.00 Wine reception

### Tuesday 30 June

10.00-11.00 JB Bost (CNRS, IHES)

*Intersection theory on arithmetic surfaces, $L^2_1$-Green functions,
and hyperbolic metrics *

11.00-11.30 Coffee

11.30-12.30 M Rapoport (Köln)

*Height pairings on Shimura curves and p-adic uniformization *

13.00-14.00 Lunch

15.00-16.00 N Dan (Paris 13)

*Analytic continuation of Green currents *

16.00-17.00 Tea

17.00-18.00 A Moriwaki (Kyoto)

*Inequalitites for semistable families of arithmetic varieties*

### Wednesday 1 July

10.00-11.00 H Tamvakis (University of Pennsylvania)

*Arithmetic Schubert calculus *

11.00-11.30 Coffee

11.30-12.30 U Tipp (Nottingham)

*A Gross-Zagier formula over function fields *

13.00-14.00 Lunch

15.00-16.00 K Köhler (Bonn)

*The arithmetic Lefschetz fixed point formula and heights *

16.00-18.30 Free time

18.30- 19.30 Reception at the Cambridge University Press bookstore

### Thursday 2 July

10.00-11.00 AJ Scholl (Durham)

*Kato's Euler systems and explicit reciprocity laws *

11.00-11.30 Coffee

11.30-12.30 SW Zhang (Columbia)

*A Gross-Zagier formula over totally real fields *

13.00-14.00 Lunch

15.00-16.00 J Kramer (Humboldt University)

*Green currents, automorphic forms and L-functions *

16.00-17.00 Tea

17.00-18.00 T Tucker (Berkeley)

*Dirichlet's theorem, Vojta's inequality, Vojta's conjecture, and related
problems *

### Friday 3 July

10.00-11.00 J Burgos (Barcelona)

*Higher Bott-Chern forms and Beilinson's regulator *

11.00-11.30 Coffee

11.30-12.30 E Ullmo (Orsay)

*Falting's height of quotients of $J_0(N)$ and related topics *

13.00-14.00 Lunch

15.00-16.00 P Michel (Orsay)

*Non-vanishing of automorphic L-functions (from the analytic point of
view) : results and applications *

16.00-17.00 Tea

17.00-18.00 M Taylor (UMIST)

*Epsilon constants of metrised line bundles *