scholarly journals Lifting and automorphy of reducible mod p Galois representations over global fields

2021 ◽  
Author(s):  
Najmuddin Fakhruddin ◽  
Chandrashekhar Khare ◽  
Stefan Patrikis
Keyword(s):  
Galois Representations ◽  
Global Fields ◽  
Mod P

scholarly journals Computing the number of certain Galois representations mod p

2011 ◽  
Vol 23 (3) ◽  
pp. 603-627 ◽  
Author(s):  
Tommaso Giorgio Centeleghe
Keyword(s):  
Galois Representations ◽  
Mod P

Hecke characters associated to Drinfeld modular forms

2015 ◽  
Vol 151 (11) ◽  
pp. 2006-2058
Author(s):  
Gebhard Böckle ◽  
Tommaso Centeleghe
Keyword(s):  
Modular Forms ◽  
Galois Representations ◽  
Close Relation ◽  
Modular Curves ◽  
Endomorphism Rings ◽  
Global Fields ◽  
Drinfeld Modular Forms ◽  
The One ◽  
Formula Type ◽  
Ordinary Reduction

In this article we explain how the results in our previous article on ‘algebraic Hecke characters and compatible systems of mod$p$Galois representations over global fields’ allow one to attach a Hecke character to every cuspidal Drinfeld modular eigenform from its associated crystal that was constructed in earlier work of the author. On the technical side, we prove along the way a number of results on endomorphism rings of${\it\tau}$-sheaves and crystals. These are needed to exhibit the close relation between Hecke operators as endomorphisms of crystals on the one side and Frobenius automorphisms acting on étale sheaves associated to crystals on the other. We also present some partial results on the ramification of Hecke characters associated to Drinfeld modular eigenforms. An important phenomenon absent from the case of classical modular forms is that ramification can also result from places of modular curves of good but non-ordinary reduction. In an appendix, jointly with Centeleghe we prove some basic results on$p$-adic Galois representations attached to$\text{GL}_{2}$-type cuspidal automorphic forms over global fields of characteristic $p$.

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