Galois representations and Cohomology of SL(3, ℤ)

Mark McConnell

doi:10.1007/3-540-58691-1_51

Galois representations and Cohomology of SL(3, ℤ)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Conjecturally, by the Langlands philosophy, a cuspidal cohomology class of level N for SL(n, ℤ) should have an attached Galois representation. This is a finite-dimensional l-adic representation π of Gal(ℚ/ℚ), unramified for primes p not dividing l and N, for which the image of a Frobenius element for p is related to the p-th Hecke eigenvalues of the class. By a conjecture of Ash [1], the same should hold for l-torsion cohomology classes α.

Original language	English (US)
Title of host publication	Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings
Editors	Leonard M. Adleman, Ming-Deh Huang
Publisher	Springer Verlag
ISBN (Print)	9783540586913
DOIs	https://doi.org/10.1007/3-540-58691-1_51
State	Published - Jan 1 1994
Externally published	Yes
Event	1st Algorithmic Number Thoery Symposium, ANTS-I 1994 - Ithaca, United States Duration: May 6 1994 → May 9 1994

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	877 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	1st Algorithmic Number Thoery Symposium, ANTS-I 1994
Country/Territory	United States
City	Ithaca
Period	5/6/94 → 5/9/94

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

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10.1007/3-540-58691-1_51

Cite this

McConnell, M. (1994). Galois representations and Cohomology of SL(3, ℤ). In L. M. Adleman, & M-D. Huang (Eds.), Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 877 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-58691-1_51

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abstract = "Conjecturally, by the Langlands philosophy, a cuspidal cohomology class of level N for SL(n, ℤ) should have an attached Galois representation. This is a finite-dimensional l-adic representation π of Gal(ℚ/ℚ), unramified for primes p not dividing l and N, for which the image of a Frobenius element for p is related to the p-th Hecke eigenvalues of the class. By a conjecture of Ash [1], the same should hold for l-torsion cohomology classes α.",

author = "Mark McConnell",

year = "1994",

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doi = "10.1007/3-540-58691-1_51",

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booktitle = "Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings",

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McConnell, M 1994, Galois representations and Cohomology of SL(3, ℤ). in LM Adleman & M-D Huang (eds), Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 877 LNCS, Springer Verlag, 1st Algorithmic Number Thoery Symposium, ANTS-I 1994, Ithaca, United States, 5/6/94. https://doi.org/10.1007/3-540-58691-1_51

Galois representations and Cohomology of SL(3, ℤ). / McConnell, Mark.
Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. ed. / Leonard M. Adleman; Ming-Deh Huang. Springer Verlag, 1994. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 877 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - Conjecturally, by the Langlands philosophy, a cuspidal cohomology class of level N for SL(n, ℤ) should have an attached Galois representation. This is a finite-dimensional l-adic representation π of Gal(ℚ/ℚ), unramified for primes p not dividing l and N, for which the image of a Frobenius element for p is related to the p-th Hecke eigenvalues of the class. By a conjecture of Ash [1], the same should hold for l-torsion cohomology classes α.

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Galois representations and Cohomology of SL(3, ℤ)

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