Non-Abelian Fundamental Groups in Arithmetic Geometry

Non-Abelian Fundamental Groups in Arithmetic Geometry's image
Created: 2009-07-29 14:30
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.

Showing results 1-20 of 93    < Prev    1 2 3 4 5    Next >
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Media items

A local analog of the Grothendieck conjectures

   934 views

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


Anabelian geometry II

   557 views

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

   297 views

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

   204 views

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

   563 views

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

   285 views

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

   444 views

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

   171 views

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

   252 views

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


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

   396 views

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

   336 views

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

   243 views

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

   214 views

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

   2,072 views

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

   214 views

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


Diophantine geometry and Galois theory 9

   1,950 views

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


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