Geometry & Topology Volume 13, issue 1 (2009)

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Congruences between modular forms given by the divided $\beta$ family in homotopy theory

Mark Behrens

Geometry & Topology 13 (2009) 319–357

DOI: 10.2140/gt.2009.13.319

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