# Non-Abelian Fundamental Groups in Arithmetic Geometry

Created: | 2009-07-29 14:30 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Description: | 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.
Read more at: http://www.newton.ac.uk/programmes/NAG/index.html EVENTS: - Introductory Workshop http://www.newton.ac.uk/programmes/NAG/nagw01.html - Anabelian Geometry http://www.newton.ac.uk/programmes/NAG/nagw02.html - Spitalfields Day - Potential Modularity http://www.newton.ac.uk/programmes/NAG/nagw05.html - Final Workshop http://www.newton.ac.uk/programmes/NAG/nagw04.html |

# Media items

This collection contains 93 media items.

### Media items

#### A local analog of the Grothendieck conjectures

Abrashkin, V (Durham)

Wednesday 12 August 2009, 14:00-15:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2009

#### A Noncommutative Iwasawa Main Conjecture for Varieties over Finite Fields

Witte, M (Regensburg)

Monday 14 December 2009, 14:00-15:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 16 Dec 2009

#### A uniform open image theorem for $\ell$-adic representations (joint work with Akio Tamagawa - R.I.M.S.)

Cadoret, A (Bordeaux 1)

Friday 28 August 2009, 14:00-15:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 4 Sep 2009

#### Anabelian geometry II

Pop, F (Pennsylvania)

Wednesday 05 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 13 Aug 2009

#### Anabelian geometry III

Pop, F (Pennsylvania)

Thursday 06 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2009

#### Anabelian geometry IV

Pop, F (Pennsylvania)

Friday 07 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2009

#### Anabelian geometry V

Nakamura, H (Okayama)

Tuesday 11 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2009

#### Anabelian geometry VI

Nakamura, H (Okayama)

Wednesday 12 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2009

#### Anabelian geometry VII

Nakamura, H (Okayama)

Thursday 13 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2009

#### Anabelian geometry VIII

Nakamura, H (Okayama)

Friday 14 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 3 Sep 2009

#### Annihilating Tate-Shafarevic groups

Burns, D (KCL)

Thursday 30 July 2009, 15:30-16:30

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 5 Aug 2009

#### Arithmetic invariants of Eisenstein type arising from fundamental groups of once punctured elliptic curves

Nakamura, H (Okayama)

Monday 14 December 2009, 15:30-16:30

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 16 Dec 2009

#### Arthur's theory of automorphic forms on classical groups (a survey)

Clozel, L (Paris-Sud 11 )

Tuesday 15 December 2009, 11:30-12:30

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 16 Dec 2009

#### Brauer-Manin obstructions for sections of the fundamental group

Stix, J (Heidelberg)

Thursday 27 August 2009, 11:00-12:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 4 Sep 2009

#### Congruences between derivatives of Artin L-functions

Burns, D (KCL)

Friday 18 December 2009, 10:15-11:15

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 18 Dec 2009

#### Conjectures on the logarithmic derivatives of Artin L-functions

Rössler, D (Paris-Sud 11)

Tuesday 15 December 2009, 15:30-16:30

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 17 Dec 2009

#### Counting l-adic representations, in the function field case

Deligne, P (IAS)

Monday 27 July 2009, 10:00-11:00

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 29 Jul 2009

#### Counting local systems with local principal unipotent monodromy

Flicker, Y (Ohio State)

Thursday 17 December 2009, 15:30-16:30

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 18 Dec 2009

#### Differences between Galois representations in automorphism and outer-automorphism groups of the fundamental group of...

Matsumoto, M (Hiroshima)

Friday 28 August 2009, 15:30-16:30

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 4 Sep 2009

#### Diophantine geometry and Galois theory 9

Kim, M (UCL)

Wednesday 16 December 2009, 11:45-12:45

**Collection**:
Non-Abelian Fundamental Groups in Arithmetic Geometry

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 17 Dec 2009