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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm102, 49 pages, doi:10.1093/imrn/rnm102 published on October 30, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

On a Generalization of the Conjecture of Mazur–Tate–Teitelbaum

Haruzo Hida

Department of Mathematics, University of California-Los Angeles, Los Angeles, CA 90095-1555, USA

Correspondence: Correspondence to be sent to: hida{at}math.ucla.edu

We propose a generalization of the conjecture of Mazur–Tate–Teitelbaum predicting an exact shape of the p-adic L-invariant of rational Tate curves (which is now a theorem of Greenberg-Stevens) to the symmetric powers of motivic two dimensional odd Galois representations over totally real fields. At p-adic places where the motive is multiplicative, the L-invariant is conjectured to have the same shape as predicted by them. Then we prove our conjecture assuming a precise ring theoretic structure of the universal infinitesimal Galois deformation ring of the symmetric power.

Communicated by Barry Mazur


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