Volume 13, issue 1 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 7, 3219–3748
Issue 6, 2675–3218
Issue 5, 2149–2674
Issue 4, 1615–2148
Issue 3, 1075–1614
Issue 2, 533–1073
Issue 1, 1–532

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Congruences between modular forms given by the divided $\beta$ family in homotopy theory

Mark Behrens

Geometry & Topology 13 (2009) 319–357
Bibliography
1 A Baker, Hecke operations and the Adams $E_2$–term based on elliptic cohomology, Canad. Math. Bull. 42 (1999) 129 MR1692001
2 M Behrens, A modular description of the $K(2)$–local sphere at the prime 3, Topology 45 (2006) 343 MR2193339
3 M Behrens, Buildings, elliptic curves, and the $K(2)$–local sphere, Amer. J. Math. 129 (2007) 1513 MR2369888
4 M Behrens, Some root invariants at the prime $2$, Geom. Topol. Monogr. 10 (2007) 1
5 M Behrens, G Laures, $\beta$–family congruences and the $f$–invariant, preprint
6 M Behrens, T Lawson, Topological automorphic forms, to appear in memoirs of the AMS
7 M Behrens, T Lawson, Isogenies of elliptic curves and the Morava stabilizer group, J. Pure Appl. Algebra 207 (2006) 37 MR2244259
8 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs 47, American Mathematical Society (1997) MR1417719
9 H Hida, $p$–adic automorphic forms on Shimura varieties, Springer Monographs in Mathematics, Springer (2004) MR2055355
10 M J Hopkins, J H Smith, Nilpotence and stable homotopy theory. II, Ann. of Math. $(2)$ 148 (1998) 1 MR1652975
11 J Hornbostel, N Naumann, Beta-elements and divided congruences, Amer. J. Math. 129 (2007) 1377 MR2354323
12 N M Katz, $p$–adic properties of modular schemes and modular forms, from: "Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)", Springer (1973) MR0447119
13 S S Kudla, From modular forms to automorphic representations, from: "An introduction to the Langlands program (Jerusalem, 2001)", Birkhäuser (2003) 133 MR1990378
14 G Laures, The Topological $q$–Expansion Principle, PhD thesis, MIT (1996)
15 G Laures, The topological $q$–expansion principle, Topology 38 (1999) 387 MR1660325
16 H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. Math. $(2)$ 106 (1977) 469 MR0458423
17 J Morava, Noetherian localisations of categories of cobordism comodules, Ann. of Math. $(2)$ 121 (1985) 1 MR782555
18 D C Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984) 351 MR737778
19 J H Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics 106, Springer (1986) MR817210
20 W C Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. $(4)$ 2 (1969) 521 MR0265369