A non-selfdual automorphic representation of GL3 and a Galois representation

Geemen, Bert van; Top, Jaap

doi:10.1007/bf01232250

Cited by 29 publications

(55 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since Gal(K 3 /K 2 ) is of order 2, Gal(K S /K 2 ) is a cyclic subgroup of Gal(K S /K). 3 Instead of looking for quadratic extensions of K 3 , we checked that cyclic extensions of order 4 of K 2 all had a too large residual degree, which proved that K 3 = K 4 and thus K S = K 3 . 4 One equation for the extension is…”

Section: Longer Versionmentioning

confidence: 99%

“…We found that the final compositum is a degree 64 field, which we denote Q (2) . In the paper [3], it is shown that the characteristic polynomial of the image of a Frobenius element Frob p depends only on its trace. As a consequence, all the eigenvalues of ρ i (Frob p ) are determined by Tr ρ i (Frob p ).…”

Section: Short Versionmentioning

confidence: 99%

“…The prime 3 is not included just because of the method (and the particular polynomial defining Q (2) ) used. Observe that all of the primes have already been checked in the paper [3].…”

Section: Short Versionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison of semi-simplifications of Galois representations

Grenié¹

2007

Journal of Algebra

View full text Add to dashboard Cite

Let Γ be the absolute Galois group of a global field. Let ρ 1 and ρ 2 be two p-adic, finite dimensional representations of Γ . Then there exists a finite number of primes q such that if the characteristic polynomials of ρ 1 (Frob q ) and ρ 2 (Frob q ) are equal, then ρ 1 and ρ 2 have isomorphic semi-simplifications and so the same L-functions. We give a method to compute a sufficient list of primes, based on the ramification and the dimension of the representations. We use then the result to prove a conjecture by B. van Geemen and J. Top.

show abstract

Section: Longer Versionmentioning

confidence: 99%

Section: Short Versionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison of semi-simplifications of Galois representations

Grenié¹

2007

Journal of Algebra

View full text Add to dashboard Cite

show abstract

“…Other tests for n=3 can be found in the work of van Geemen and Top with van der Kallen and Verberkmoes [27][28][29][30]. The purpose of this paper is to make the first computational tests of this conjecture for n=4.…”

mentioning

confidence: 95%

Cohomology of Congruence Subgroups of SL4(Z)

Ash¹,

Gunnells²,

McConnell³

2002

Journal of Number Theory

View full text Add to dashboard Cite

Let N > 1 be an integer, and let C=C 0 (N) … SL 4 (Z) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H 5 (C; C) for a range of N and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the BorelSerre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4. © 2002 Elsevier Science (USA)

show abstract

“…These symbols have allowed many researchers to fruitfully explore the numbertheoretic significance of this cohomology group, especially for n = 2 and 3 [3,7,5,20,21]. For all their power, though, modular symbols have limitations:…”

Section: 1mentioning

confidence: 99%

Modular Symbols and Hecke Operators

Gunnells

2000

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.

show abstract

A non-selfdual automorphic representation of GL3 and a Galois representation

Cited by 29 publications

References 5 publications

Comparison of semi-simplifications of Galois representations

Comparison of semi-simplifications of Galois representations

Cohomology of Congruence Subgroups of SL4(Z)

Modular Symbols and Hecke Operators

Contact Info

Product

Resources

About