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Special Collection in Honor of Robert F. Coleman

RobertColeman-padicConfPicRobert Coleman was one of the 20th century’s most influential number theorists. His ideas have influenced arithmetic geometry and the field of modular forms. He unexpectedly passed away a few years ago. This special collection has been assembled in his memory.

Edited by: Matt Baker (Georgia Institute of Technology), Barry Mazur (Harvard University), and Kenneth Ribet (University of California Berkeley) 

 

 

  1. Research

    On the rigid cohomology of certain Shimura varieties

    We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of http://static-content.springer.com/image/art%3A10.1186%2Fs40687-016-0078-5/40687_2016_78_Article_IEq1.gif

    Michael Harris, Kai-Wen Lan, Richard Taylor and Jack Thorne

    Research in the Mathematical Sciences 2016 3:37

    Published on: 26 October 2016

  2. Research

    Rankin–Eisenstein classes in Coleman families

    We show that the Euler system associated with Rankin–Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in p-adic Coleman fami...

    David Loeffler and Sarah Livia Zerbes

    Research in the Mathematical Sciences 2016 3:29

    Published on: 1 October 2016

  3. Research

    The adic, cuspidal, Hilbert eigenvarieties

    We construct adic, compactified eigenvarieties parameterizing adic overconvergent Hilbert modular eigenforms of finite slope by constructing integral families of modular sheaves on the relevant formal Shimura ...

    Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni

    Research in the Mathematical Sciences 2016 3:34

    Published on: 8 September 2016

  4. Research

    Elliptic curves of rank two and generalised Kato classes

    Heegner points play an outstanding role in the study of the Birch and Swinnerton-Dyer conjecture, providing canonical Mordell–Weil generators whose heights encode first derivatives of the associated Hasse–Weil L-...

    Henri Darmon and Victor Rotger

    Research in the Mathematical Sciences 2016 3:27

    Published on: 24 August 2016

  5. Research

    On the regulator formulas of Bertolini, Darmon and Rotger

    We give a unified, and somewhat simplified, account of the regulator formulas appearing in papers of Bertolini, Darmon and Rotger, describing the syntomic regulator on the first, second and third self-products...

    Amnon Besser

    Research in the Mathematical Sciences 2016 3:26

    Published on: 22 August 2016

  6. Research

    New methods for \((\varphi, \Gamma)\)-modules

    We provide new proofs of two key results of p-adic Hodge theory: the Fontaine-Wintenberger isomorphism between Galois groups in characteristic 0 and characteristic p, and the Cherbonnier–Colmez theorem on decompl...

    Kiran S Kedlaya

    Research in the Mathematical Sciences 2015 2:20

    Published on: 16 October 2015

    The Erratum to this article has been published in Research in the Mathematical Sciences 2015 2:25