The Fifth Montreal-Toronto Workshop in Number Theory.
April 18-19, 2013, CRM Montreal.
Organizers: Eyal Goren (McGill) and Steve Kudla (Toronto)

The Fifth Montreal-Toronto Workshop is devoted to p-divisible groups. Funding for these events is provided by the CRM and Fields Institutes.

The lectures will take place at the lecture hall on the 6-th floor of the CRM (Pavillon Andre Aisenstadt, room 6214). Here is a precise schedule.

All participants are requested to register. Registration is free, but mandatory. All participants are requested to let us know at time of registration whether they want to come to Thursday dinner on  night (that will be significantly subsidized, but not free). Please indicate it in the "further information" field. It is important for the CRM to collect this information, and for us
when we apply to renew our funding.

Register here in English
Register here in French

Wednesday:
Arrival of the Toronto delegation.
Informal discussions.



 

Title

Details

Speaker

Time

 

Coffee and Refreshments (pastries, fruits)


 

Thursday

9:00 - 9:30

1

Definitions and main examples

The categories of finite p-torsion groups schemes and p-divisible groups. Isogenies and duals. Where do p-divisible groups arise? (abelian varieties, formal groups, ...) Catalogue of the p-divisible groups arising from abelian varieties of dimension at most 3. The Ekedahl-Oort stratification for ppav.

Dylan Attwell-Duval

Thursday

9:30-10:20

2

Witt vectors and the Dieudonne ring

Witt vectors: sketch of construction and main properties.  Topology.  Definition of the Dieudonn'e ring and its Euclidean property. The Cartier ring (time allowing).

Luiz Takei

Thursday

10:30 - 11:10

 

Coffee break (with basic cookies)


 

Thursday

11:10 - 11:30

3

Dieudonne modules.

The equivalence of categories for p-divisible and for p-torsion group schemes. The construction of the Dieudonn’e module (sketch).

Patrick Walls

Thursday

11:30 - 12:20

 

Lunch break

We are each on our own.

 

 

4

Classification of p-divisible groups up to isogeny. 

 

Classical Dieudonn'e classification. Kottwitz's formuation and Newton strata for PEL Shimura varieties.

Andrew Fiori

Thursday

2:30 - 3:20

5

Deformations, crystals and Grothendieck-Messing theory 

 

Ying Zong

Thursday

3:30 - 4:20

 

Coffee break (with basic cookies and fruits)


 

Thursday

4:20 - 4:50

6

The Serre-Tate theorems

The theorem about deforming abelian varieties and deforming p-divisible groups. Serre-Tate coordinates. Applications.

Amy Cheung

Thursday

4:50 - 5:35

7

Kisin modules

 

Francesca Bergamaschi

Thursday

5:45 - 6:30

 

 

 

 

 

 

Coffee and Refreshments (pastries, fruits)


 

Friday

9:00 - 9:30

8

Stratification of Unitary Shimura varieties

(and another version of notes)

 

Steve Kudla

Friday

9:30–11:00

 

Coffee break (with basic cookies)


 

Friday

11:00 - 11:30

9

Stratifications of moduli spaces and p-adic uniformization 

The Newton, Ekedahl Oort and Hodge stratifications. Rapoport-Zink spaces. Connection to variation of zeta functions, to tautological classes and to the Langlands correspondence.

Eyal Goren

Friday

11:30-13:00