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Mathematics Colloquium
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سمینار عمومی ریاضیات
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TITLE
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Shtukas and the Analogy Between Number Fields and Function Fields
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SPEAKER
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Esmail Arasteh Rad
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University of Muenster, Germany and National Center for Theoretical Sciences (NCTS), Taiwan
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TIME
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Monday, December 14, 2020,
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16:00 - 17:00
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VENUE |
(Online)
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SUMMARY |
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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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تهران، ضلع جنوبی
ميدان شهيد باهنر (نياوران)، پژوهشگاه
دانشهای بنيادی، پژوهشکده رياضيات
School of
Mathematics, Institute for Research in
Fundamental Sciences (IPM), Niavaran
Bldg., Niavaran Square, Tehran
ipmmath@ipm.ir
♦ +98 21
22290928 ♦
math.ipm.ir |
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