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Mathematics Colloquium سمینار عمومی ریاضیات




TITLE  
Shtukas and the Analogy Between Number Fields and Function Fields


SPEAKER  
Esmail Arasteh Rad  
University of Muenster, Germany and National Center for Theoretical Sciences (NCTS), Taiwan  
 


TIME  
Monday, December 14, 2020,   16:00 - 17:00


VENUE   (Online)



SUMMARY

 

During the last decades lots of efforts have been invested in developing A. Weil's discourse on the analogy in mathematics. This method essentially aims to bring number theory into the light of geometry, through a bridge called the arithmetic of function fields. In this context, and as it may be observed through Langlands philosophy, moduli spaces (/stacks) for global G-shtukas appear as analogs for Shimura varieties, and consequently, they play a crucial role in Langlands program over function fields. They possess local counterparts which are called Rapoport-Zink spaces for local P-shtukas (i.e. function fields analogs for Rapoport-Zink spaces for p-divisible groups). In this talk we overview the landscape of this analogy, by translating Deligne's conception of Shimura varieties (as a moduli for motives) to the realm of function fields. We explain some results in this direction and some further results related to the deformation theory and local model theory for the moduli of G-shtukas. If time permits we also discuss some of the applications.

Joining info: Join with Google Meet:
meet.google.com/shg-corg-gwr

 




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