Duke Mathematical Journal
- Duke Math. J.
- Volume 129, Number 2 (2005), 337-369.
Mod ℓ representations of arithmetic fundamental groups, I: An analog of Serre's conjecture for function fields
There is a well-known conjecture of Serre that any continuous, irreducible representation which is odd arises from a newform. Here is the absolute Galois group of , and is an algebraic closure of the finite field of of ℓ elements. We formulate such a conjecture for -dimensional mod ℓ representations of for any positive integer and where is a geometrically irreducible, smooth curve over a finite field of characteristic (), and we prove this conjecture in a large number of cases. In fact, a proof of all cases of the conjecture for follows from a result announced by Gaitsgory in [G]. The methods are different.
Duke Math. J., Volume 129, Number 2 (2005), 337-369.
First available in Project Euclid: 27 September 2005
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F80: Galois representations 11F70: Representation-theoretic methods; automorphic representations over local and global fields 14H30: Coverings, fundamental group [See also 14E20, 14F35] 11R34: Galois cohomology [See also 12Gxx, 19A31]
Böckle, Gebhard; Khare, Chandrashekhar. Mod ℓ representations of arithmetic fundamental groups, I: An analog of Serre's conjecture for function fields. Duke Math. J. 129 (2005), no. 2, 337--369. doi:10.1215/S0012-7094-05-12925-8. https://projecteuclid.org/euclid.dmj/1127831441