HSAGA研讨班

发布时间:2024-09-23浏览次数:54


Contact: 郭宁    (guon314 1@mail.ustc.edu.cn)        黄可平  (kphuang@hit.edu.cn)

             刘春晖 (chunhui.liu@hit.edu.cn)              田乙胜    (tysmath@mail.ustc.edu.cn)

             王珺    (junwangmath@hit.edu.cn )           赵和耳    (heerzhao@hit.edu.cn)    


Upcoming talks


October 9th, 14:30-16:00 pm (Beijing time

Speaker: 阳煜 (京都大学数理解析研究所)

Title: Fundamental groups of curves and local moduli

Abstract

   

In 1996, A. Tamagawa discovered a surprising phenomenon: anabelian geometry also exists for curves over algebraically closed fields of characteristic p>0 (i.e., curves in positive characteristic can possibly be determined by their geometric fundamental groups without relying on Galois actions). However, after 28 years, only a few results have emerged in this field. In this talk, I want to explain the following insight of the speaker about fundamental groups of curves in positive characteristic: 


The (admissible or geometric log etale) fundamental groups of pointed stable curves over algebraically closed fields of characteristic p can be regarded as an analogue of local moduli spaces of the curves. 


This observation led to the speaker discovering some new kinds of anabelian phenomena of curves in characteristic p and to formulated numerious new conjectures. For example, the following highly non-trivial anbelian results of the speaker provide strong evidence supporting this insight:

 The homeomorphism conjecture holds for 1-dimensional moduli spaces (roughly speaking, this conjecture means that the moduli spaces of curves can be reconstructed group-theoretically as topological spaces).

• A new proof of Mochizuki’s famous result concerning (Isom-version) Grothendieck’s anabelian conjecture for curves over sub-p-adic fields without using Faltings’ p-adic Hodge theory.

• The group-theoretical specialization conjecture holds (roughly speaking, this conjecture means that the topological and group-theoretical degeneration of curves can be completely determined by open continuous homomorphisms of dmissible fundamental groups).





October 10th, 10:30-12:00 am (Beijing time

Speaker: 陈升 (长春理工大学)

Title: Arithmetic purity of strong approximation for complete toric varieties

Abstract

    In this talk, I will discuss arithmetic purity of strong approximation: motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.




Past talks


September 12th, 14:30-16:30 pm (Beijing time

Speaker: 张旭成(清华大学丘成桐数学中心)

Title: A stacky approach to identifying the stability condition

Abstract

    For any reductive group we find a stacky interpretation of the stability condition for principal bundles over a curve: it is the unique maximal open locus that admits a schematic moduli space. Some applications and further progress will be discussed. This is a joint work with Dario Weissmann and Andres Fernandez Herrero.






August 7th, 16:45-17:45 pm (Beijing time

Speaker: 吕昌(中国科学院)

Title: Brauer-Manin obstruction of finite product of some algebraic stacks

Abstract

    I shall start from a classical result on Brauer-Manin obstruction of a product of two varieties, by introducing Yang Cao's formulas of Kunneth type. Then we will generalize it to a class of algebraic stacks.





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