Weights in Serre's conjecture for GLn via the Bernstein-Gelfand-Gelfand complex

Michael M. Schein

doi:10.1016/j.jnt.2008.03.008

Weights in Serre's conjecture for GL_n via the Bernstein-Gelfand-Gelfand complex

Michael M. Schein

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let ρ : Gal (over(Q, -) / Q) → GL_n (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 GL_n formulated by Ash, Doud, Pollack, Sinnott, and Herzig; to our knowledge, this is the first unconditional evidence for these conjectures for arbitrary n.

Original language	English
Pages (from-to)	2808-2822
Number of pages	15
Journal	Journal of Number Theory
Volume	128
Issue number	10
DOIs	https://doi.org/10.1016/j.jnt.2008.03.008
State	Published - Oct 2008
Externally published	Yes

Keywords

Crystalline cohomology
Galois representations
Serre's conjecture

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10.1016/j.jnt.2008.03.008

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title = "Weights in Serre's conjecture for GLn via the Bernstein-Gelfand-Gelfand complex",

abstract = "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.",

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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

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ER -

Weights in Serre's conjecture for GL_n via the Bernstein-Gelfand-Gelfand complex

Abstract

Keywords

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