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.

Nontrivial Elements of Sha Explained through K3 Surfaces

Adam Logan and Ronald Van Luijk
Mathematics of Computation
Vol. 78, No. 265 (Jan., 2009), pp. 441-483
Stable URL: http://www.jstor.org/stable/40234783
Page Count: 43
  • Read Online (Free)
  • Download ($34.00)
  • 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.
Nontrivial Elements of Sha Explained through K3 Surfaces
Preview not available

Abstract

We present a new method to show that a principal homogeneous space of the Jacobian of a curve of genus two is nontrivial. The idea is to exhibit a Brauer- Manin obstruction to the existence of rational points on a quotient of this principal homogeneous space. In an explicit example we apply the method to show that a specific curve has infinitely many quadratic twists whose Jacobians have nontrivial Tate-Shafarevich group.

Page Thumbnails

  • Thumbnail: Page 
441
    441
  • Thumbnail: Page 
442
    442
  • Thumbnail: Page 
443
    443
  • Thumbnail: Page 
444
    444
  • Thumbnail: Page 
445
    445
  • Thumbnail: Page 
446
    446
  • 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
  • Thumbnail: Page 
465
    465
  • Thumbnail: Page 
466
    466
  • Thumbnail: Page 
467
    467
  • Thumbnail: Page 
468
    468
  • Thumbnail: Page 
469
    469
  • Thumbnail: Page 
470
    470
  • Thumbnail: Page 
471
    471
  • Thumbnail: Page 
472
    472
  • Thumbnail: Page 
473
    473
  • Thumbnail: Page 
474
    474
  • Thumbnail: Page 
475
    475
  • Thumbnail: Page 
476
    476
  • Thumbnail: Page 
477
    477
  • Thumbnail: Page 
478
    478
  • Thumbnail: Page 
479
    479
  • Thumbnail: Page 
480
    480
  • Thumbnail: Page 
481
    481
  • Thumbnail: Page 
482
    482
  • Thumbnail: Page 
483
    483