You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Study of the Local Components of the Hecke Algebra mod l
Transactions of the American Mathematical Society
Vol. 270, No. 1 (Mar., 1982), pp. 253-267
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1999771
Page Count: 15
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
We use information about modular forms mod l to study the local structure of the Hecke ring. In particular, we find nontrivial lower bounds for the dimensions of the Zariski tangent spaces of the local components of the Hecke ring mod l. These results suggest that the local components of the Hecke ring mod l are more complex than originally expected. We also investigate the inverse limits of the Hecke rings of weight k mod l as K varies within a fixed congruence class mod l - 1. As an immediate corollary to some of the above results, we show that when k is sufficiently large, an arbitrary prime l must divide the index of the classical Hecke ring Tk in the ring of integers of Tk ⊗ Q.
Transactions of the American Mathematical Society © 1982 American Mathematical Society