Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This 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.

The Main Conjecture for CM Elliptic Curves at Supersingular Primes

Robert Pollack and Karl Rubin
Annals of Mathematics
Second Series, Vol. 159, No. 1 (Jan., 2004), pp. 447-464
Published by: Annals of Mathematics
Stable URL: http://www.jstor.org/stable/3597257
Page Count: 18
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
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.
The Main Conjecture for CM Elliptic Curves at Supersingular Primes
Preview not available

Abstract

At a prime of ordinary reduction, the Iwasawa "main conjecture" for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is similar in structure to the ordinary case. Namely, Kobayashi's conjecture relates modified Selmer groups, which he defined, with modified p-adic L-functions defined by the first author. In this paper we prove Kobayashi's conjecture for elliptic curves with complex multiplication.

Page Thumbnails

  • Thumbnail: Page 
[447]
    [447]
  • Thumbnail: Page 
448
    448
  • Thumbnail: Page 
449
    449
  • Thumbnail: Page 
450
    450
  • Thumbnail: Page 
451
    451
  • Thumbnail: Page 
452
    452
  • Thumbnail: Page 
453
    453
  • Thumbnail: Page 
454
    454
  • Thumbnail: Page 
455
    455
  • Thumbnail: Page 
456
    456
  • Thumbnail: Page 
457
    457
  • Thumbnail: Page 
458
    458
  • Thumbnail: Page 
459
    459
  • Thumbnail: Page 
460
    460
  • Thumbnail: Page 
461
    461
  • Thumbnail: Page 
462
    462
  • Thumbnail: Page 
463
    463
  • Thumbnail: Page 
464
    464