ETHZ-UZh-Sbg Arithmetic and Geometry Research Group

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**Workshop "Periods and heights of CM abelian varieties"**

This workshop is organized by J. Ayoub, C. Fuchs, A. Kresch and G. Wüstholz. It takes place from July 6-11, 2014 at the Böglerhof in Alpbach/Tyrol, Austria.

This summer school will continue a many-year tradition of schools in Alpbach featuring high-profile research results in arithmetic and geometry. The topic builds on p-adic periods from the ProDoc Workshop 2010. PhD students/postdocs (mainly from Zurich) present the topics, and everyone gains a deep exposure.

Colmez' conjecture relates the Faltings height, measuring the complexity of a CM abelian variety, to L-functions, which are generalizations of the Riemann zeta-function. For a CM elliptic curve (CM, or complex multiplication, refers to extra symmetries), the conjecture reproduces the Chowla-Selberg formula. The goal of the workshop is to understand Colmez' proof, which treats the case of abelian CM fields. More detailes on the program will be published here in due time.

A pre-workshop took place at FIM from April 7-10, 2014. For further details see here.

**Participants:**

Joseph Ayoub

Marco Besier (Mainz)

Peter Bruin (Warwick)

Simon Felten (Mainz)

Andrea Ferraguti

Javier Fresan (Bonn)

Clemens Fuchs (Salzburg)

Martin Gallauer

Sergey Gorchinskiy (Moscow)

Daniel Harrer (Freiburg)

Christoph Hutle (Salzburg)

Ariyan Javanpeykar (Mainz)

Peter Jossen (Lausanne)

Rafael von Känel (MPI Bonn)

Andrew Kresch

Lars Kühne (Pisa)

Vincent Maillot (Paris)

Matthias Nickel (Mainz)

Roland Paulin (Salzburg)

Simon Pepin-Lehalleur

Maximilian Preisinger (Mainz)

Michael Rottmaier (Freiburg)

Sonia Samol (Mainz)

Max Schmidtke (Freiburg)

Vaibhav Vaish

Francesco Veneziano (Graz)

Alberto Vezzani

Konrad Völkel (Freiburg)

Thomas Weißschuh (Mainz)

Gisbert Wüstholz

The participants consist of PhD students and postdocs in arithmetic and geometry from Zurich as well as colleagues from Bonn, Freiburg, Graz, Lausanne, Mainz, Moscow, Pisa, Salzburg and Warwick.

**Program:**

The program will start on Sunday evening, the first talk is scheduled for 17:15-18:45. The detailed program of the planned talks will be published here: Program-2014

(Tentative) Schedule:

09:00 - 10:30: First talk

10:30 - 11:00: Coffee break

11:00 - 12:30: Second talk

12:45: Lunch

13:45 - 15:15: Third talk

15:30 - 18:00: Time for informal discussion

19:00: Dinner

**Lecture Notes and Literature:**

Program written by Damian Rössler (version from April 7, 2014): Program-2014

Suitable references can be found here.

Back to the main page.

This workshop is organized by J. Ayoub, C. Fuchs, A. Kresch and G. Wüstholz. It takes place from July 6-11, 2014 at the Böglerhof in Alpbach/Tyrol, Austria.

This summer school will continue a many-year tradition of schools in Alpbach featuring high-profile research results in arithmetic and geometry. The topic builds on p-adic periods from the ProDoc Workshop 2010. PhD students/postdocs (mainly from Zurich) present the topics, and everyone gains a deep exposure.

Colmez' conjecture relates the Faltings height, measuring the complexity of a CM abelian variety, to L-functions, which are generalizations of the Riemann zeta-function. For a CM elliptic curve (CM, or complex multiplication, refers to extra symmetries), the conjecture reproduces the Chowla-Selberg formula. The goal of the workshop is to understand Colmez' proof, which treats the case of abelian CM fields. More detailes on the program will be published here in due time.

A pre-workshop took place at FIM from April 7-10, 2014. For further details see here.

Joseph Ayoub

Marco Besier (Mainz)

Peter Bruin (Warwick)

Simon Felten (Mainz)

Andrea Ferraguti

Javier Fresan (Bonn)

Clemens Fuchs (Salzburg)

Martin Gallauer

Sergey Gorchinskiy (Moscow)

Daniel Harrer (Freiburg)

Christoph Hutle (Salzburg)

Ariyan Javanpeykar (Mainz)

Peter Jossen (Lausanne)

Rafael von Känel (MPI Bonn)

Andrew Kresch

Lars Kühne (Pisa)

Vincent Maillot (Paris)

Matthias Nickel (Mainz)

Roland Paulin (Salzburg)

Simon Pepin-Lehalleur

Maximilian Preisinger (Mainz)

Michael Rottmaier (Freiburg)

Sonia Samol (Mainz)

Max Schmidtke (Freiburg)

Vaibhav Vaish

Francesco Veneziano (Graz)

Alberto Vezzani

Konrad Völkel (Freiburg)

Thomas Weißschuh (Mainz)

Gisbert Wüstholz

The participants consist of PhD students and postdocs in arithmetic and geometry from Zurich as well as colleagues from Bonn, Freiburg, Graz, Lausanne, Mainz, Moscow, Pisa, Salzburg and Warwick.

The program will start on Sunday evening, the first talk is scheduled for 17:15-18:45. The detailed program of the planned talks will be published here: Program-2014

Sunday, 06.07.2014: Arrival day - Introduction and overview Introductory talk (Fresan) |

Monday: The periods mod bar{Q}^* Deligne's theorem on absolute Hodge cycles on abelian varities (Pepin-Lehallleur); Andersons's period distribution, Shimura's monomial relations and the gamma distribution; Fermat curves (Vaish), proof of Anderson's theorem (Preisinger/Samol/Weißschuh) |

Tuesday: Formal groups Commutative formal groups, the Dieudonne and Tate modules of a commutative formal group, Tate's results (Vezzani); Lubin-Tate formal groups (Ferraguti); CM formal groups, the main structure theorem (Paulin/Hutle/Veneziano) |

Wednesday: The p-adic periods of CM formal groups p-adic periods for CM formal groups (Gallauer) Possible afternoon program: Informal discussion, excursions, hiking tours |

Thursday: Colmez's period distribution and formulation of the main theorem Crystalline cohomology, the action of the crystalline Weil group (Harrer/Rottmaier/Schmidtke); p-adic absolute Hodge cycles (Jossen); the period distribution ht, the main result, link with the Faltings height (Javanpeykar) |

Friday, 11.07.2014: Fermat curves, completion of the proof and outlook Colemans's result on the action of the crystalline Weil group on the cohomology of Fermat curves, completion of the proof (Bruin); complements: the motivic setting (Gorchinskiy); complements: the logarithmic derivatives of Dirichlet L-functions at negative integers (Maillot) |

(Tentative) Schedule:

09:00 - 10:30: First talk

10:30 - 11:00: Coffee break

11:00 - 12:30: Second talk

12:45: Lunch

13:45 - 15:15: Third talk

15:30 - 18:00: Time for informal discussion

19:00: Dinner

Program written by Damian Rössler (version from April 7, 2014): Program-2014

Suitable references can be found here.

Impressum 21.03.2016