Iwasawa Theory for p-torsion Class Group Schemes in Characteristic p
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Iwasawa Theory for p-torsion Class Group Schemes in Characteristic p

Time: 09:30 to  11:00 Ngày 15/02/2022

Venue/Location: Online

Speaker: Jeremy Booher, University of Canterbury

Content:
A Zp tower of curves in characteristic p is a sequence C_0, C_1, C_2, ... of smooth projective curves over a perfect field of characteristic p such that C_n is a branched cover of C_{n-1} and C_n is a branched Galois Z/(p^n)-cover of C_0. The genus is a well-understood invariant of algebraic curves, and the genus of C_n can be seen to depend on n in a simple fashion. In characteristic p, there are additional curve invariants like the a-number which are poorly understood. They describe the group-scheme structure of the p-torsion of the Jacobian. I will discuss work with Bryden Cais studying these invariants and suggesting that their growth is also "regular" in Zp towers. This is a new kind of Iwasawa theory for function fields.
 
Hình thức: Online qua Zoom.