Entrance hall of the ICMS

Non-commutative algebra and Iwasawa theory

Sep 28, 2009 - Oct 02, 2009

14 India Street, Edinburgh EH3 6EZ

Organisers

Name Institution
Brown, Ken A University of Glasgow
Burns, David King's College London
Coates, John University of Cambridge
Schneider, Peter Universität Münster

The aim of the workshop will be to discuss related recent developments in non-commutative algebra and Iwasawa theory. Iwasawa theory, via its main conjectures, remains the only systematic method known today for studying the mysterious connexions between purely arithmetic problems and special values of complex L-functions, typified by the conjecture of Birch and Swinnerton-Dyer. There is ever growing evidence that these main conjectures hold in vast generality, in particular, for all motives over p-adic Lie extension of number fields. At the same time, the Iwasawa algebras of compact p-adic Lie groups provide one of the most interesting examples of non-commutative rings. It is now clear that, intertwined with the arithmetic problems of Iwasawa theory, many intriguing questions of non-commutative algebra arise, which are interesting in their own right, and whose solution could eventually be very useful for understanding some of the classical problems of number theory. The Workshop will have lectures by both number-theorists and experts in non-commutative algebra, aimed at explaining to each other their results, conjectures, and hopes for future work.

This workshop is organised by ICMS as a satellite meeting of the Isaac Newton Institute, Cambridge.

Arrangements

Participation
Participation is by invitation only.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and, if so, how to apply for one. If you do require a visa, ICMS can provide a signed invitation letter.

Venue
The workshop will take place at ICMS, 14 India Street, Edinburgh, EH3 6EZ. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.

The seminar room at 14 India Street has whiteboards, 2 overhead projectors, a data projector and laptop. We ask that you use our ICMS laptop for your presentation which you may bring on a memory stick or CD.

Wireless access is available throughout the building. There are also 4 public PCs which may be used at any time for internet access and to check email.

Travel
The ICMS travel pages contain advice on how to travel to Edinburgh. For local information, the finding ICMS page shows the location of ICMS and contains useful maps of the city centre. If you asked ICMS to book hotel accommodation for you, this map shows the location of The Ballantrae Albany Hotel in relation to the workshop venue at ICMS.

There are major roadworks taking place in Edinburgh at present due to the installation of tram tracks throughout the city centre. You are advised to travel by public transport and not by car as parking is very difficult to find and may prove expensive.

Accommodation
If you requested that ICMS arrange your accommodation, you will have been notified by email of the Ballantrae Albany Hotel details and the nights booked on your behalf. If you have not received an email with the details, please contact Audrey Brown at ICMS. The hotel will invoice ICMS directly so you will not be asked to pay the bed and breakfast costs. For information, this map shows The Ballantrae Albany Hotel.

Alternatively, participants are free to make their own arrangements and may claim back the cost, with receipts, up to a maximum of £65.00 per night bed and breakfast for a maximum of 6 nights. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.

Meals and Refreshments
Morning and afternoon refreshments will be provided on each day of the workshop.

On Monday 28 September and Friday 2 October, a light buffet lunch will be provided free of charge to participants in the Exhibition Room at 14 India Street. On Tuesday, Wednesday and Thursday participants are free to explore the many cafés, sandwich shops, restaurants and bars nearby.

Following the lectures on Monday 28 September, there will be an informal wine reception in the Exhibition Room at 14 India Street.

After the wine reception on Monday 28 September, at 18.00, all participants are invited to an evening meal in Ristorante Librizzi (Sicilian/Italian) Restaurant, 69 North Castle Street, Edinburgh. A further informal meal will take place on Tuesday 29 September at 19.00 in The Nargile (Turkish) Restaurant, 73 Hanover Street, Edinburgh. A Workshop Dinner will be held on the evening of Thursday 1 October at 19.00 in The Magnum (Scottish) Restaurant, 1 Albany Street, Edinburgh (map showing location of restaurants) The workshop grant will cover the cost of these meals.

Registration
Registration will take place between 09.00 and 09.45 on the morning of Monday 28 September in the Exhibition Room at 14 India Street. There is no registration fee.

Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your bed and breakfast accommodation, tea/coffee Monday to Friday, lunch on Monday and Friday only, a short wine reception on Monday following the talks, the informal meals on Monday and Tuesday evening and the Workshop Dinner on Thursday evening.

If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop directly through the Isaac Newton Institute (INI). At Registration, you will be issued with an INI travel claim form - please note that receipts or other supporting documentation are required for the travel costs claimed.

Programme

This workshop will start at 09.00 on Monday 28 September and finish with lunch 12.00-14.00 on Friday 2 October 2009.

Monday 28 September

09.00 - 09.45

Registration and coffee

09.45 - 10.00

Introduction and welcome

10.00 - 11.00

Peter Schneider (Universität Münster)
K_1 and generalized Coleman maps

11.00 - 11.30

Coffee/tea break

11.30 - 12.30

Simon Wadsley (University of Cambridge)
Euler characteristics and Iwasawa algebras

12.30 - 14.00

Lunch provided in the Exhibition Room

14.00 - 15.00

Karl Rubin (University of California, Irvine)
Refined class number formulas and Kolyvagin systems

15.00 - 15.30

Coffee/tea break

15.30 - 16.30

Sarah Zerbes (University of Exeter)
The higher Hilbert pairing via (phi,G)-modules

16.30 - 17.45

Wine Reception in the Exhibition Room at ICMS

18.00

Informal meal at Ristorante (Sicilian/Italian) Librizzi, 69 North Castle Street, Edinburgh

 

Tuesday 29 September

09.30 - 10.30

Romyar Sharifi (University of Arizona)
Selmer groups and reducible representations

10.30 - 11.00

Coffee/tea break

11.00 - 12.00

Annette Huber-Klawitter (University of Freiburg)
p-adic Borel regulators and Tamagawa numbers

12.00 - 14.00

Lunch break

14.00 - 15.00

Konstantin Ardakov (University of Nottingham)
Roseblade's Theorem D for Iwasawa algebras

15.00 - 15.30

Coffee/tea break

15.30 - 16.30

Christopher Brookes (University of Cambridge)
Deformation spaces for pro-p groups and Iwasawa algebras

19.00

Informal evening meal at Nargile (Turkish) Restaurant, 73 Hanover Street, Edinburgh

 

Wednesday 30 September

09.30 - 10.30

Irene Lau (Universität Augsburg)
On the structure of the Iwasawa algebra

10.30 - 11.00

Coffee/tea break

11.00 - 12.00

Mahesh Kakde (University College London)
Computation of K_1 of non-commutative groups rings

12.00

Lunch break and free afternoon

 

Thursday 1 October

09.30 - 10.30

Ramdorai Sujatha (Tata Institute of Fundamental Research)
Non-commutative Iwasawa theory in Hida families

10.30 - 11.00

Coffee/tea break

11.00 - 12.00

Takashi Hara (University of Tokyo)
Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p

12.00 - 14.00

Lunch break

14.00 - 15.00

Otmar Venjakob (University of Heidelberg)
On localisations of skew power series rings

15.00 - 15.30

Coffee/tea break

15.30 - 16.30

Jürgen Ritter (University of Augsburg)
Toward a proof of the 'main conjecture' of equivariant Iwasawa theory

19.00

Workshop dinner at The Magnum (Scottish) Restaurant, 1 Albany Street, Edinburgh
(dress informal)

 

Friday 2 October

09.30 - 10.30

Fabien Trihan (University of Nottingham)
On an analogue of the Iwasawa Main Conjecture for abelian varieties over function fields of characteristic p>0

10.30 - 11.00

Coffee/tea break

11.00 - 12.00

John Coates (University of Cambridge)
On studying the Tate-Shafarevich group of elliptic curves with complex multiplication via Iwasawa theory

12.00 - 14.00

Lunch provided in the Exhibition Room, 14 India Street, Edinburgh



Presentations:

Presentation Details
Ardakov, Konstantin
Roseblade's Theorem D for Iwasawa algebras
View Abstract Down
Brookes, Christopher
Deformation spaces for pro-p groups and Iwasawa algebras
View Abstract Down
Coates, John
On studying the Tate-Shafarevich group of elliptic curves with complex multiplication via Iwasawa theory
View Abstract Down
Hara, Takashi
Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p
View Abstract Down
Huber-Klawitter, Annette
p-adic Borel regulators and Tamagawa numbers
View Abstract Down
Kakde, Mahesh
Computation of K_1 of non-commutative groups rings
View Abstract Down
Lau, Irene
On the structure of the Iwasawa algebra
View Abstract Down
Ritter, Jürgen
Toward a proof of the 'main conjecture' of equivariant Iwasawa theory
View Abstract Down
Rubin, Karl
Refined class number formulas and Kolyvagin systems
View Abstract Down
Schneider, Peter
K_1 and generalized Coleman maps
View Abstract Down
Sharifi, Romyar
Selmer groups and reducible representations
View Abstract Down
Sujatha, Ramdorai
Non-commutative Iwasawa theory in Hida families
View Abstract Down
Trihan, Fabien
On an analogue of the Iwasawa Main Conjecture for abelian varieties over function fields of characteristic p>0
View Abstract Down
Venjakob, Otmar
On localisations of skew power series rings
View Abstract Down
Wadsley, Simon
Euler characteristics and Iwasawa algebras
View Abstract Down
Zerbes, Sarah
The higher Hilbert pairing via (phi,G)-modules
View Abstract Down

Participants

Name Institution
Ardakov, Konstantin University of Nottingham
Bouganis, Athanasios University of Heidelberg
Brookes, Christopher University of Cambridge
Brown, Ken A University of Glasgow
Coates, John University of Cambridge
Hara, Takashi University of Tokyo
Huber-Klawitter, Annette University of Freiburg
Kakde, Mahesh University College London
Kang, Yunling Nanjing University
Lau, Irene Universität Augsburg
Lechner, Sabine University of Freiburg
Liang, Zhibin Capital Normal University
Ritter, Jürgen University of Augsburg
Rubin, Karl University of California, Irvine
Schneider, Peter Universität Münster
Sharifi, Romyar University of Arizona
Sujatha, Ramdorai Tata Institute of Fundamental Research
Trihan, Fabien University of Nottingham
Venjakob, Otmar University of Heidelberg
Wadsley, Simon University of Cambridge
Witte, Malte Universität Regensburg
Zerbes, Sarah University of Exeter