scholarly journals Weights in Serre's conjecture for GLn via the Bernstein–Gelfand–Gelfand complex

2008 ◽  
Vol 128 (10) ◽  
pp. 2808-2822
Author(s):  
Michael M. Schein
Keyword(s):  
Serre's Conjecture ◽  
Serre’S Conjecture

Algorithmic aspects of Suslin's proof of Serre's conjecture

1993 ◽  
Vol 3 (1) ◽  
pp. 31-55 ◽  
Author(s):  
Leandro Caniglia ◽  
Guillermo Corti�as ◽  
Silvia Dan�n ◽  
Joos Heintz ◽  
Teresa Krick ◽  
...  
Keyword(s):  
Serre's Conjecture ◽  
Serre’S Conjecture

scholarly journals SERRE WEIGHTS FOR LOCALLY REDUCIBLE TWO-DIMENSIONAL GALOIS REPRESENTATIONS

2014 ◽  
Vol 14 (3) ◽  
pp. 639-672 ◽  
Author(s):  
Fred Diamond ◽  
David Savitt
Keyword(s):  
Galois Representations ◽  
Real Field ◽  
Two Dimensional ◽  
Serre's Conjecture ◽  
Weight Part ◽  
Totally Real ◽  
Serre’S Conjecture ◽  
Totally Real Field

Let $F$ be a totally real field, and $v$ a place of $F$ dividing an odd prime $p$. We study the weight part of Serre’s conjecture for continuous totally odd representations $\overline{{\it\rho}}:G_{F}\rightarrow \text{GL}_{2}(\overline{\mathbb{F}}_{p})$ that are reducible locally at $v$. Let $W$ be the set of predicted Serre weights for the semisimplification of $\overline{{\it\rho}}|_{G_{F_{v}}}$. We prove that, when $\overline{{\it\rho}}|_{G_{F_{v}}}$ is generic, the Serre weights in $W$ for which $\overline{{\it\rho}}$ is modular are exactly the ones that are predicted (assuming that $\overline{{\it\rho}}$ is modular). We also determine precisely which subsets of $W$ arise as predicted weights when $\overline{{\it\rho}}|_{G_{F_{v}}}$ varies with fixed generic semisimplification.

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