THE EISENSTEIN IDEAL of WEIGHT k and RANKS of HECKE ALGEBRAS

Deo, SV (2024) THE EISENSTEIN IDEAL of WEIGHT k and RANKS of HECKE ALGEBRAS. In: Journal of the Institute of Mathematics of Jussieu, 23 (2). pp. 983-1017.

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Abstract

Let p and � be primes such that p > 3 and p|�-1 and k be an even integer. We use deformation theory of pseudo-representations to study the completion of the Hecke algebra acting on the space of cuspidal modular forms of weight k and λ0(�) level at the maximal Eisenstein ideal containing p. We give a necessary and sufficient condition for the Zp-rank of this Hecke algebra to be greater than in terms of vanishing of the cup products of certain global Galois cohomology classes. We also recover some of the results proven by Wake and Wang-Erickson for k = 2 using our methods. In addition, we prove some R = T theorems under certain hypotheses. © The Author(s), 2023. Published by Cambridge University Press.

Item Type:	Journal Article
Publication:	Journal of the Institute of Mathematics of Jussieu
Publisher:	Cambridge University Press
Additional Information:	The copyright for this article belongs to publishers.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	18 Nov 2024 16:14
Last Modified:	18 Nov 2024 16:14
URI:	http://eprints.iisc.ac.in/id/eprint/86757

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