3
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      On Siegel eigenvarieties at Saito-Kurokawa points

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We study the geometry of the Siegel eigenvariety EΔ of paramodular tame level Δ associated to a squarefree NN+ at certain points having a critical slope. For k2 let f be a cuspidal eigenform of S2k2(Γ0(N)) ordinary at a prime pN with sign ϵf=1 and write α for the unit root of the Hecke polynomial of f at p. Let SK(f)α be the semi-ordinary p-stabilization of the Saito-Kurokawa lift of the cusp form f to GSp(4) of weight (k,k) of tame level Δ. Under the assumption that the dimension of the Selmer group H1f,unr(Q,ρf(k1)) attached to f is at most one and some mild assumptions on the mod p representation ˉρf associated to f, we show that the rigid analytic space EΔ is smooth at the point x corresponding to SK(f)α. This means that there exists a unique irreducible component of EΔ specializing to x, and we also show that this irreducible component is not globally endoscopic. Finally we give an application to the Bloch-Kato conjecture, by proving under some mild assumptions on ˉρf that the smoothness failure of EΔ at x yields that dimH1f,unr(Q,ρf(k1))2.

          Related collections

          Most cited references4

          • Record: found
          • Abstract: not found
          • Article: not found

          On ordinary ?-adic representations associated to modular forms

          D A Wiles (1988)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            On thel-adic cohomology of Siegel threefolds

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              SUR LES DÉFORMATIONS p-ADIQUES DE CERTAINES REPRÉSENTATIONS AUTOMORPHES

                Bookmark

                Author and article information

                Journal
                15 February 2019
                Article
                1902.05885
                80387062-ddfa-4c32-a613-8fb3012311ec

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                11F33, 11F46, 11F80, 14G22
                45 pages (plus 15 pages appendices)
                math.NT

                Number theory
                Number theory

                Comments

                Comment on this article