TY - JOUR
T1 - Weights in Serre's conjecture for GLn via the Bernstein-Gelfand-Gelfand complex
AU - Schein, Michael M.
PY - 2008/10
Y1 - 2008/10
N2 - Let ρ : Gal (over(Q, -) / Q) → GLn (over(F, -)p) be an n-dimensional mod p Galois representation. If ρ is modular for a weight in a certain class, called p-minute, then we restrict the Fontaine-Laffaille numbers of ρ; in other words, we specify the possibilities for the restriction of ρ to inertia at p. Our result agrees with the Serre-type conjectures for GLn formulated by Ash, Doud, Pollack, Sinnott, and Herzig; to our knowledge, this is the first unconditional evidence for these conjectures for arbitrary n.
AB - Let ρ : Gal (over(Q, -) / Q) → GLn (over(F, -)p) be an n-dimensional mod p Galois representation. If ρ is modular for a weight in a certain class, called p-minute, then we restrict the Fontaine-Laffaille numbers of ρ; in other words, we specify the possibilities for the restriction of ρ to inertia at p. Our result agrees with the Serre-type conjectures for GLn formulated by Ash, Doud, Pollack, Sinnott, and Herzig; to our knowledge, this is the first unconditional evidence for these conjectures for arbitrary n.
KW - Crystalline cohomology
KW - Galois representations
KW - Serre's conjecture
UR - http://www.scopus.com/inward/record.url?scp=49849090756&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2008.03.008
DO - 10.1016/j.jnt.2008.03.008
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AN - SCOPUS:49849090756
SN - 0022-314X
VL - 128
SP - 2808
EP - 2822
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 10
ER -