On the homotopy type of the spectrum representing elliptic cohomology

Author:
Andrew Baker

Journal:
Proc. Amer. Math. Soc. **107** (1989), 537-548

MSC:
Primary 55N22; Secondary 11F11

DOI:
https://doi.org/10.1090/S0002-9939-1989-0982399-6

MathSciNet review:
982399

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we analyse the homotopy type at primes of the ring spectrum representing a version of elliptic cohomology whose coefficient ring agrees with the ring of modular forms for . For any prime (=maximal) graded ideal containing the Eisenstein function as well as , we show that there is a morphism of ring spectra

**[Ad]**J. F. Adams,*Stable homotopy and generalised homology*, University of Chicago Press, Chicago. MR**1324104 (96a:55002)****[Ba 1]**A. Baker,*Hecke operators as operations in elliptic cohomology*, preprint, 1988. MR**1037690 (91m:55005)****[Ba 2]**-,*Elliptic cohomology*,*-adic modular forms and Atkin's operator*, preprint, 1988.**[BaWü]**A. Baker and U. Würgler,*Liftings of formal group laws and the Artinian completion of*, preprint, 1988.**[Ig 1]**J. Igusa,*On the transformation theory of elliptic functions*, Amer. J. Math.**81**(1959), 436-52. MR**0104668 (21:3421)****[Ig 2]**-,*On the algebraic theory of elliptic modular functions*, J. Math. Soc. Japan**20**(1968), 96-106. MR**0240103 (39:1457)****[Ka]**N. Katz,*-adic properties of modular schemes and modular forms*, Lecture Notes in Mathematics**350**(1973), 69-190. MR**0447119 (56:5434)****[Ko]**N. Koblitz,*Introduction to elliptic curves and modular forms*, Springer-Verlag, New York. MR**766911 (86c:11040)****[Land 1]**P. S. Landweber,*Elliptic cohomology and modular forms*, Lecture Notes in Mathematics**1326**(1988), 55-68. MR**970281****[Land 2]**-,*Supersingular elliptic curves and congruences for Legendre polynomials*, Lecture Notes in Mathematics**1326**(1988), 69-93. MR**970282****[Ma]**H. Matsumura,*Commutative ring theory*, Cambridge University Press, Cambridge. MR**879273 (88h:13001)****[Rav]**D. C. Ravenel,*Complex cobordism and the stable homotopy Groups of spheres*, Academic Press, London. MR**860042 (87j:55003)****[Se 1]**J.-P. Serre,*Cours d'arithmétique*, Presses Universitaires de France, Vendôme.**[Se 2]**-,*Formes modulaires et fonctions zeta**-adiques*, Lecture Notes in Mathematics**350**(1973), 191-268. MR**0404145 (53:7949a)****[Se 3]**-,*Congruences et formes modulaires*, Séminaire Bourbaki, Vol 24, no. 416, Lecture Notes in Mathematics**317**(1971/2), 319-38.**[Si]**J. Silverman,*The arithmetic of elliptic curves*, Springer-Verlag, New York.**[Ya]**N. Yagita,*The exact functor theorem for*, Proc. Jap. Acad.**52**(1976), 1-3. MR**0394631 (52:15432)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
55N22,
11F11

Retrieve articles in all journals with MSC: 55N22, 11F11

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0982399-6

Keywords:
Elliptic cohomology,
-Periodicity,
Morava -theory

Article copyright:
© Copyright 1989
American Mathematical Society