Non-abelian fundamental groups in arithmetic geometry

Programme theme

In the 1980's Grothendieck formulated his anabelian conjectures that brought to an hitherto-unexplored depth the interaction between topology and arithmetic. This suggested that the study of non-abelian fundamental groups could lead to a new understanding of deep arithmetic phenomena, including the arithmetic theory of moduli and Diophantine finiteness on hyperbolic curves. A certain amount of work in recent years linking fundamental groups to Diophantine geometry intimates deep and mysterious connections to the theory of motives and Iwasawa theory, with their links with arithmetic problems on special values of L-functions such as the conjecture of Birch and Swinnerton-Dyer. In fact, the work thus far suggests that the still-unresolved section conjecture of Grothendieck, whereby maps from Galois groups of number fields to fundamental groups of arithmetic curves are all proposed to be of geometric origin, is exactly the sort of key problem that touches the core of all these areas of number theory and more.

The goal of this programme is to investigate the ideas and problems of anabelian geometry within the global context of mainstream arithmetic geometry. By bringing together leading experts in number theory and arithmetic geometry we hope to shed more light on the inter-connections between anabelian geometry and more classical Diophantine problems, and hopefully make progress towards the solution of the section conjecture.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero Authors: Yuichiro Hoshi Download PDF	2009	NAG

Title

Year

Programme

Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero

Authors: Yuichiro Hoshi

Download PDF

2009

NAG

Workshops

NAGW01

Seminars

Monday 3rd August 2009
17:00 to 18:00	Pierre Deligne Institute for Advanced Study, Princeton Cohomology of algebraic varieties	Room 1

Tuesday 4th August 2009
11:00 to 12:00	Florian Pop University of Pennsylvania Anabelian geometry I	Room 1
14:00 to 15:00	Scott Corry Lawrence University The pro-$p$ Hom-form of the birational anabelian conjecture	Room 1

Wednesday 5th August 2009
11:00 to 12:00	Florian Pop University of Pennsylvania Anabelian geometry II	Room 1

Thursday 6th August 2009
11:00 to 12:00	Florian Pop University of Pennsylvania Anabelian geometry III	Room 1
16:00 to 18:00	Informal discussions	Discussion Room

Friday 7th August 2009
11:00 to 12:00	Florian Pop University of Pennsylvania Anabelian geometry IV	Room 1

Monday 10th August 2009
14:30 to 15:30	Pierre Deligne Institute for Advanced Study, Princeton Multiple zeta values 1	Room 1
16:00 to 17:00	Pierre Deligne Institute for Advanced Study, Princeton Multiple zeta values II	Room 1

Tuesday 11th August 2009
11:00 to 12:00	Hiroaki Nakamura Okayama University Anabelian geometry V	Room 1
14:00 to 15:00	Alina Vdovina Newcastle University Fundamental groups of CW-complexes from different points of view	Room 1

Wednesday 12th August 2009
11:00 to 12:00	Hiroaki Nakamura Okayama University Anabelian geometry VI	Room 1
14:00 to 15:00	Victor Abrashkin Durham University A local analog of the Grothendieck conjectures	Room 1

Thursday 13th August 2009
11:00 to 12:00	Hiroaki Nakamura Okayama University Anabelian geometry VII	Room 1
16:00 to 18:00	Informal discussions	Discussion Room

Friday 14th August 2009
11:00 to 12:00	Hiroaki Nakamura Okayama University Anabelian geometry VIII	Room 1

Monday 17th August 2009
14:30 to 15:30	Pierre Deligne Institute for Advanced Study, Princeton Mulitple zeta values III	Room 2
16:00 to 17:00	Pierre Deligne Institute for Advanced Study, Princeton Multiple zeta values IV	Room 2

Tuesday 18th August 2009
11:00 to 12:00	Mohamed Saidi University of Exeter Anabelian geometry IX	Room 2
14:00 to 15:00	Victor Abrashkin Durham University A local analog of the Grothendieck conjectures	Room 2

Wednesday 19th August 2009
11:00 to 12:00	Mohamed Saidi University of Exeter Anabelian geometry X	Room 2

Thursday 20th August 2009
11:00 to 12:00	Mohamed Saidi University of Exeter Anabelian geometry XI	Room 2
14:30 to 15:30	Uwe Jannsen Universität Regensburg Canonical embedded resolution of singularities for two-dimensional schemes	Room 2

Friday 21st August 2009
11:00 to 12:00	Mohamed Saidi University of Exeter Anabelian geometry XII	Room 2
14:30 to 15:30	Pierre Deligne Institute for Advanced Study, Princeton Multiple zeta values V	Room 2
16:00 to 18:00	Mahesh Kakde University College London Discussion session	Discussion Room
16:00 to 17:00	Pierre Deligne Institute for Advanced Study, Princeton Multiple zeta values VI	Room 2

Tuesday 1st September 2009
11:00 to 12:00	Peter Schneider The algebraic theory of p-adic Lie groups I	Room 1

Wednesday 2nd September 2009
11:00 to 12:00	Peter Schneider The algebraic theory of p-adic Lie groups II	Room 1

Thursday 3rd September 2009
11:00 to 12:00	Peter Schneider The algebraic theory of p-adic Lie groups III	Room 1

Monday 7th September 2009
11:00 to 12:00	Christophe Breuil IHES On the p-adic Langlands programme for GL2(F) I: Construction of representation of GL(2)F over bar F p	Room 1

Tuesday 8th September 2009
10:00 to 11:00	Peter Schneider The algebraic theory of p-adic Lie groups IV	Room 1
11:30 to 12:30	Christophe Breuil IHES On the p-adic Langlands programme for GL(2) F II: (phi, Gamma)-modules over barmathbb F p and tensor induction	Room 1

Wednesday 9th September 2009
10:00 to 11:00	Peter Schneider The algebraic theory of p-adic Lie groups V	Room 1
11:30 to 12:30	Christophe Breuil IHES On the p-adic Langlands programme for GL(2)F III: Qp-locally analytic representations of GL(2)F and crystalline representations	Room 1

Thursday 10th September 2009
10:00 to 11:00	Peter Schneider The algebraic theory of p-adic Lie groups VI	Room 1
11:30 to 12:30	Christophe Breuil IHES On the p-adic Langlands programme for GL(2)F IV: The Hodge filtration and speculation on extra components	Room 1

Tuesday 15th September 2009
10:00 to 11:00	Peter Schneider The algebraic theory of p-adic Lie groups VII	Room 1
11:30 to 12:30	John Coates University of Cambridge Iwasawa theory of elliptic curves over p-adic Lie extensions of dimension greater than 1 - I	Room 1

Wednesday 16th September 2009
10:00 to 11:00	Peter Schneider The algebraic theory of p-adic Lie groups VIII	Room 1
11:30 to 12:30	Sujatha Ramdorai Tata Institute of Fundamental Research Iwasawa theory of elliptic curves over p-adic Lie extensions of dimension greater than 1 - II	Room 1

Thursday 17th September 2009
10:00 to 11:00	Peter Schneider The algebraic theory of p-adic Lie groups IX	Room 1
11:30 to 12:30	Sujatha Ramdorai Tata Institute of Fundamental Research Iwasawa theory of elliptic curves over p-adic Lie extensions of dimension greater than 1 - III	Room 1

Monday 21st September 2009
11:00 to 12:00	John Coates University of Cambridge Iwasawa theory of elliptic curves over p-adic Lie extensions of dimension greater than 1 - IV	Room 1

Tuesday 22nd September 2009
11:00 to 12:00	Peter Schneider The algebraic theory of p-adic Lie groups X	Room 1

Wednesday 23rd September 2009
11:00 to 12:00	Peter Schneider The algebraic theory of p-adic Lie groups XI	Room 1

Thursday 24th September 2009
11:00 to 12:00	Peter Schneider The algebraic theory of p-adic Lie groups XII	Room 1

Monday 5th October 2009
14:00 to 15:00	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - I	Room 1
15:30 to 16:30	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - II	Room 1

Tuesday 6th October 2009
11:00 to 12:00	Leila Schneps Relations between multi-zeta values and Grothendieck-Teichmueller theory	Room 1

Wednesday 7th October 2009
14:00 to 15:00	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - III	Room 1
15:30 to 16:30	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - IV	Room 1

Monday 12th October 2009
14:00 to 15:00	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - V	Room 1
15:30 to 16:30	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - VI	Room 1

Friday 16th October 2009
14:00 to 15:00	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - VII	Room 1
15:30 to 16:30	Hoil Kim Kyungpook National University Motivic fundamental groups and diophantine geometry - VIII	Room 1

Thursday 22nd October 2009
14:00 to 16:00	David Loeffler University of Cambridge P-ADIC analysis	Discussion Room

Thursday 29th October 2009
14:00 to 16:00	David Loeffler University of Cambridge P-ADIC analysis	Discussion Room

Monday 2nd November 2009
09:30 to 12:00	NAG informal discussions	Discussion Room

Tuesday 3rd November 2009
09:30 to 12:00	NAG informal discussions	Room 2

Wednesday 4th November 2009
09:30 to 12:00	NAG informal discussions	Discussion Room

Thursday 5th November 2009
09:30 to 13:00	NAG informal discussions	Discussion Room
14:00 to 15:00	Mehrdad Shahshahani IPM - Institute for Studies in Theoretical Physics and Mathematics Constructing dessin d'enfants on curves	Room 1

Friday 6th November 2009
09:30 to 13:00	NAG informal discussions	Discussion Room

Monday 9th November 2009
14:00 to 15:30	Mahesh Kakde University College London The main conjectures of Iwasawa theory I	Room 1
16:00 to 17:00	Mahesh Kakde University College London The main conjectures of Iwasawa theory II	Room 1

Monday 16th November 2009
14:00 to 15:30	Mahesh Kakde University College London The main conjectures of Iwasawa theory III	Room 1
16:00 to 17:00	Mahesh Kakde University College London The main conjectures of Iwasawa theory IV	Room 1

Wednesday 18th November 2009
14:00 to 15:00	Mahesh Kakde University College London The main conjectures of Iwasawa theory V	Room 1
16:00 to 17:00	Mahesh Kakde University College London The main conjectures of Iwasawa theory VI	Room 1

Thursday 19th November 2009
11:00 to 12:00	Pierre Lochak Université Pierre et Marie Curie Paris Topological methods in Grothendieck-Teichmueller theory	Room 1

Monday 23rd November 2009
14:00 to 15:00	Zdzislaw Wojtkowiak CNRS (Centre national de la recherche scientifique) Periods of Tate motives, examples, Galois side	Room 1

Wednesday 25th November 2009
14:00 to 15:00	Don Blasius University of California, Los Angeles Work of Chenevier and Chenevier-Clozel	Room 1

Thursday 26th November 2009
14:00 to 15:00	Don Blasius University of California, Los Angeles Work of Chenevier and Cheniever-Clozel II	Room 2
16:00 to 17:00	Yoshitaka Hachimori Tokyo University of Science Euler characteristics of fine Selmer groups	Room 2

Monday 30th November 2009
14:00 to 15:00	Hoil Kim Kyungpook National University Iwasawa theory for supersingular primes: for a larger class of abelian varieties and multi-variable Iwasawa theory	Room 1

Wednesday 2nd December 2009
11:00 to 12:00	Marco Antei Université des Sciences et Technologies de Lille On the abelian fundamental group scheme of a family of varieties	Room 1
14:00 to 15:00	Andrew Wiles Princeton University Bigness and modularity lifting	Room 1

Thursday 3rd December 2009
14:00 to 16:00	David Loeffler University of Cambridge P-adic analysis	Room 2

Friday 4th December 2009
11:00 to 12:00	Cristian Popescu University of California, San Diego The Galois module structure of p-adic realisations of Picard 1-motives and applications	Room 1

Non-abelian fundamental groups in arithmetic geometry

Organisers

John Coates University of Cambridge
Florian Pop University of Pennsylvania
Mohamed Saidi Aalborg Universitet
Peter Schneider

Speakers

Victor Abrashkin Durham University
Marco Antei Université des Sciences et Technologies de Lille
Don Blasius University of California, Los Angeles
Christophe Breuil IHES
John Coates University of Cambridge
Scott Corry Lawrence University
Pierre Deligne Institute for Advanced Study, Princeton
Yoshitaka Hachimori Tokyo University of Science
Uwe Jannsen Universität Regensburg
Mahesh Kakde University College London
Hoil Kim Kyungpook National University
Pierre Lochak Université Pierre et Marie Curie Paris
David Loeffler University of Cambridge
Hiroaki Nakamura Okayama University
Florian Pop University of Pennsylvania
Cristian Popescu University of California, San Diego
Sujatha Ramdorai Tata Institute of Fundamental Research
Mohamed Saidi Aalborg Universitet
Peter Schneider
Leila Schneps
Mehrdad Shahshahani IPM - Institute for Studies in Theoretical Physics and Mathematics
Alina Vdovina Newcastle University
Andrew Wiles Princeton University
Zdzislaw Wojtkowiak CNRS (Centre national de la recherche scientifique)

Show All

Non-abelian fundamental groups in arithmetic geometry

Programme theme

Preprints

Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero

Workshops

Non-abelian fundamental groups in arithmetic geometry - introductory workshop

Anabelian geometry

Non-commutative algebra and non-commutative Iwasawa theory

Potential modularity (Spitalfields day)

Final workshop

Seminars

Organisers

Speakers

Supported By

Non-abelian fundamental groups in arithmetic geometry

Programme theme

Preprints

Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero

Workshops

Non-abelian fundamental groups in arithmetic geometry - introductory workshop

Anabelian geometry

Non-commutative algebra and non-commutative Iwasawa theory

Potential modularity (Spitalfields day)

Final workshop

Seminars

Organisers

Speakers

Supported By

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