scholarly journals Unipotent groups associated to reduced curves

2000 ◽  
Vol 352 (11) ◽  
pp. 5025-5043
Author(s):  
David Penniston
Keyword(s):  
2016 ◽  
Vol 152 (8) ◽  
pp. 1697-1724 ◽  
Author(s):  
Tanmay Deshpande

In this paper, we extend the notion of Shintani descent to general (possibly disconnected) algebraic groups defined over a finite field $\mathbb{F}_{q}$. For this, it is essential to treat all the pure inner $\mathbb{F}_{q}$-rational forms of the algebraic group at the same time. We prove that the notion of almost characters (introduced by Shoji using Shintani descent) is well defined for any neutrally unipotent algebraic group, i.e. an algebraic group whose neutral connected component is a unipotent group. We also prove that these almost characters coincide with the ‘trace of Frobenius’ functions associated with Frobenius-stable character sheaves on neutrally unipotent groups. In the course of the proof, we also prove that the modular categories that arise from Boyarchenko and Drinfeld’s theory of character sheaves on neutrally unipotent groups are in fact positive integral, confirming a conjecture due to Drinfeld.


2015 ◽  
pp. 561-580
Author(s):  
Brian Conrad ◽  
Ofer Gabber ◽  
Gopal Prasad

2010 ◽  
Vol 16 (4) ◽  
pp. 857-933 ◽  
Author(s):  
Mitya Boyarchenko

2011 ◽  
pp. 473-493
Author(s):  
Brian Conrad ◽  
Ofer Gabber ◽  
Gopal Prasad

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