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Constructing semisimple p-adic Galois representations with prescribed properties
| Content Provider | Semantic Scholar |
|---|---|
| Author | Khare, Chandrashekhar Larsen, Michael Ramakrishna, Ravi S. |
| Copyright Year | 2003 |
| Abstract | The study of p-adic representations of absolute Galois groups of number fields, i.e., continuous representations ρ : GK → GLn(Qp) with GK the absolute Galois group of a number field and p a prime, is one of the central themes of modern number theory. The ones studied the most are those which arise from the étale cohomology of smooth, projective varieties over number fields. These have the striking property (due to Weil, Dwork, Grothendieck et al.) that they are ramified at finitely many primes and are rational over a number field L, i.e., for all primes r that are not ramified in ρ, the characteristic polynomial attached to the conjugacy class of Frobr in the image of ρ (with Frobr the Frobenius substitution at r) has coefficients in L[X]. Each belongs to a compatible family of Galois representations and is pure of some weight k. In this paper we give a purely Galois theoretic method for constructing semisimple continuous representations ρ : GK → GLn(Qp) that are density ∗some of the work on this paper was done during a visit to Université Paris 7 which was supported by Centre franco-indien pour la promotion de la recherche avancée (CEFIPRA) under Project 2501-1 Algebraic Groups in Arithmetic and Geometry †partially supported by NSF Grant DMS-0100537 ‡partially supported by NSF Grant DMS-0102173 and the AMS Centennial Research Fellowship. The author thanks UC-Berkeley and Princeton University for their hospitality during visits in 2003. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://mlarsen.math.indiana.edu/~larsen/papers/klr.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0309283v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Characteristic polynomial Coefficient Cynthia Dwork IBM Notes Linear algebra Nephrogenic Systemic Fibrosis Status Epilepticus Theory UC Browser VHDL-AMS |
| Content Type | Text |
| Resource Type | Article |
