$\Lambda$-adic Barsotti–Tate groups

Haruzo Hida

Vol. 268 (2014), No. 2, 283–312

DOI: 10.2140/pjm.2014.268.283

Abstract

We define $\Lambda$-BT groups as well-controlled ind-Barsotti–Tate groups under the action of the Iwasawa algebra and construct a prototypical example of such groups out of modular Jacobians. We then discuss the relation of these groups to Weil numbers of weight $1$ and to the nonvanishing problem of the adjoint $\mathcal{ℒ}$-invariant.

To my dear friend Jon Rogawski, who created the UCLA number theory group.

Keywords

Hecke algebra, Galois representation, Galois deformation, Barsotti–Tate group

Mathematical Subject Classification 2010

Primary: 11F11, 11F25, 11F33, 11F80, 14L05

Secondary: 11F32

Milestones

Received: 23 June 2013

Revised: 28 October 2013

Accepted: 2 December 2013

Published: 21 June 2014