Arithmetic of a singular K3 surface
Matthias Schütt
Source: Michigan Math. J. Volume 56, Issue 3
(2008), 513-527.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.mmj/1231770357
Digital Object Identifier: doi:10.1307/mmj/1231770357
Mathematical Reviews number (MathSciNet): MR2488723
Zentralblatt MATH identifier: 1163.14022
References
M. Artin, Supersingular $K3$ surfaces, Ann. Sci. École Norm. Sup. (4) 7 (1974), 543--568.
Mathematical Reviews (MathSciNet): MR371899
J. W. S. Cassels, Lectures on elliptic curves, London Math. Soc. Stud. Texts, 24, Cambridge Univ. Press, Cambridge, 1991.
Mathematical Reviews (MathSciNet): MR1144763
I. Dolgachev and D. Kond\B o, A supersingular $K3$ surface in characteristic 2 and the Leech lattice, Internat. Math. Res. Notices 1 (2003), 1--23.
K. Ireland and M. Rosen, A classical introduction to modern number theory, Grad. Texts in Math., 84, Springer-Verlag, Berlin, 1982.
Mathematical Reviews (MathSciNet): MR661047
H. Ito, On extremal elliptic surfaces in characteristic 2 and 3, Hiroshima Math. J. 32 (2002), 179--188.
Mathematical Reviews (MathSciNet): MR1925896
Project Euclid: euclid.hmj/1151007555
R. Livné, Motivic orthogonal two-dimensional representations of $\text\rm Gal(\bar\Bbb Q/\Bbb Q),$ Israel J. Math. 92 (1995), 149--156.
Mathematical Reviews (MathSciNet): MR1357749
Digital Object Identifier: doi:10.1007/BF02762074
Q. Liu, D. Lorenzini, and M. Raynaud, On the Brauer group of a surface, Invent. Math. 159 (2005), 673--676.
Mathematical Reviews (MathSciNet): MR2125738
Digital Object Identifier: doi:10.1007/s00222-004-0403-2
R. Miranda and U. Persson, On extremal rational elliptic surfaces, Math. Z. 193 (1986), 537--558.
Mathematical Reviews (MathSciNet): MR867347
Digital Object Identifier: doi:10.1007/BF01160474
M. Schütt, CM newforms with rational coefficients, Ramanujan J. (to appear).
------, Hecke eigenforms and the arithmetic of singular K3 surfaces, Ph.D. thesis, Univ. Hannover, 2006.
------, Elliptic fibrations of some extremal K3 surfaces, Rocky Mountain J. Math. 37 (2007), 609--652.
Mathematical Reviews (MathSciNet): MR2333389
Digital Object Identifier: doi:10.1216/rmjm/1181068770
Project Euclid: euclid.rmjm/1181068770
I. Shimada and D. Q. Zhang, Classification of extremal elliptic $K3$ surfaces and fundamental groups of open $K3$ surfaces, Nagoya Math. J. 161 (2001), 23--54.
Mathematical Reviews (MathSciNet): MR1820211
Project Euclid: euclid.nmj/1114631551
T. Shioda, On the Mordell--Weil lattices, Comment. Math. Univ. St. Paul. 39 (1990), 211--240.
Mathematical Reviews (MathSciNet): MR1081832
------, The elliptic K3 surfaces with a maximal singular fibre, C. R. Acad. Sci. Paris Sér. I Math. 337 (2003), 461--466.
Mathematical Reviews (MathSciNet): MR2023754
Digital Object Identifier: doi:10.1016/j.crma.2003.07.007
J. H. Silverman, Advanced topics in the arithmetic of elliptic curves, Grad. Texts in Math., 151, Springer-Verlag, New York, 1994.
Mathematical Reviews (MathSciNet): MR1312368
J. Tate, On the conjectures of Birch and Swinnerton--Dyer and a geometric analog, Dix exposés sur la cohomologie des schemas (A. Grothendieck, N. H. Kuiper, eds.), pp. 189--214, North-Holland, Amsterdam, 1968.
------, Conjectures on algebraic cycles in $\ell$-adic cohomology, Proc. Sympos. Pure Math., 55, pp. 71--83, Amer. Math. Soc., Providence, RI, 1994.
The Michigan Mathematical Journal
