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An overview of abelian varieties in homotopy theory
Tyler Lawson

Geometry & Topology Monographs 16
(2009) 179–214

1 
J F Adams,
Stable homotopy and generalised homology, University of
Chicago Press (1974) MR0402720 
2 
M Ando, M J
Hopkins, N P Strickland, Elliptic spectra, the
Witten genus and the theorem of the cube, Invent. Math.
146 (2001) 595–687 MR1869850 
3 
A Baker, Hecke
operators as operations in elliptic cohomology, J. Pure
Appl. Algebra 63 (1990) 1–11 MR1037690 
4 
T Bauer, Computation of the
homotopy of the spectrum tmf, from: "Groups, homotopy
and configuration spaces (Tokyo 2005)" (editors N Iwase, T
Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13 (2008)
11–40 
5 
M Behrens, Notes on the construction of
tmf, Preprint 
6 
M Behrens, A modular
description of the K(2)–local sphere at the prime
3, Topology 45 (2006) 343–402 MR2193339 
7 
M Behrens, T
Lawson, Topological automorphic forms, To appear in
Mem. Amer. Math. Soc. 
8 
M Behrens, T
Lawson, Topological automorphic forms on U(1,1)
Submitted 
9 
A K Bousfield,
On the homotopy
theory of K–local spectra at an odd prime, Amer.
J. Math. 107 (1985) 895–932 MR796907 
10 
P Deligne, Courbes
elliptiques: formulaire d'après J. Tate, from:
"Modular functions of one variable, IV (Proc Internat. Summer
School, Univ. Antwerp, Antwerp, 1972)", Springer (1975)
MR0387292 
11 
P Deligne, M
Rapoport, Les schémas de modules de courbes
elliptiques, from: "Modular functions of one variable, II
(Proc Internat. Summer School, Univ. Antwerp, Antwerp, 1972)",
Lecture Notes in Math. 349, Springer (1973) 143–316
MR0337993 
12 
E S Devinatz,
M J Hopkins, Homotopy
fixed point spectra for closed subgroups of the Morava
stabilizer groups, Topology 43 (2004) 1–47
MR2030586 
13 
E S Devinatz,
M J Hopkins, J H Smith, Nilpotence and stable
homotopy theory I, Ann. of Math. (2) 128 (1988)
207–241 MR960945 
14 
G Faltings,
C L Chai, Degeneration of abelian varieties,
Ergebnisse Series 22, Springer (1990) MR1083353
With an appendix by David Mumford 
15 
J Franke, Uniqueness theorems
for certain triangulated categories with an Adams spectral
sequence (1996) 
16 
P G Goerss,
(Pre)sheaves of ring spectra over the moduli stack of
formal group laws, from: "Axiomatic, enriched and motivic
homotopy theory", NATO Sci. Ser. II Math. Phys. Chem. 131,
Kluwer (2004) 101–131 MR2061853 
17 
P Goerss, H W
Henn, M Mahowald, C Rezk, A resolution of
the K(2)–local sphere at the prime 3, Ann. of Math.
(2) 162 (2005) 777–822 MR2183282 
18 
P G Goerss,
M J Hopkins, Moduli spaces of commutative ring
spectra, from: "Structured ring spectra", London Math. Soc.
Lecture Note Ser. 315, Cambridge Univ. Press (2004)
151–200 MR2125040 
19 
V Gorbounov, M
Mahowald, Formal
completion of the Jacobians of plane curves and higher real
K–theories, J. Pure Appl. Algebra 145 (2000)
293–308 MR1733427 
20 
M Harris, R
Taylor, The geometry and cohomology of some simple
Shimura varieties, Annals of Mathematics Studies 151,
Princeton University Press (2001) MR1876802
With an appendix by Vladimir G Berkovich 
21 
H W Henn, On
finite resolutions of K(n)–local spheres, from:
"Elliptic cohomology", London Math. Soc. Lecture Note Ser. 342,
Cambridge Univ. Press (2007) 122–169 MR2330511 
22 
S Hollander, A
homotopy theory for stacks, Israel J. Math. 163 (2008)
93–124 MR2391126 
23 
M J Hopkins,
Complex oriented cohomology theories and the language of
stacks (1999) 
24 
M J Hopkins,
Algebraic topology and modular forms, from: "Proceedings
of the International Congress of Mathematicians, Vol I
(Beijing, 2002)", Higher Ed. Press (2002) 291–317
MR1989190 
25 
M Hovey, N P
Strickland, Morava K–theories and
localisation, (1999) MR1601906 
26 
N Katz,
Serre–Tate local moduli, from: "Algebraic surfaces
(Orsay, 1976–78)", Lecture Notes in Math. 868, Springer
(1981) 138–202 MR638600 
27 
R E Kottwitz,
Points on some
Shimura varieties over finite fields, J. Amer. Math.
Soc. 5 (1992) 373–444 MR1124982 
28 
P S Landweber,
Homological
properties of comodules over MU_{*}(MU) and
BP_*(BP), Amer. J. Math. 98 (1976) 591–610
MR0423332 
29 
P S Landweber,
D C Ravenel, R E Stong, Periodic
cohomology theories defined by elliptic curves, from: "The
\v Cech centennial (Boston, MA, 1993)", Contemp. Math. 181,
Amer. Math. Soc. (1995) 317–337 MR1320998 
30 
G Laumon, L
MoretBailly, Champs algébriques, Ergebnisse
Series 39, Springer (2000) MR1771927 
31 
M Mahowald, C
Rezk, Topological modular forms of level 3, To
appear in Pure and Applied Math. Quarterly 
32 
J P May,
Idempotents and Landweber exactness in brave new
algebra, Homology Homotopy Appl. 3 (2001) 355–359
MR1856031 
33 
W Messing, The
crystals associated to Barsotti–Tate groups: with
applications to abelian schemes, Lecture Notes in
Mathematics 264, Springer (1972) MR0347836 
34 
J S Milne,
Points on Shimura varieties mod p, from: "Automorphic
forms, representations and L–functions (Proc. Sympos.
Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part
2", Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc. (1979)
165–184 MR546616 
35 
J Milnor, On the cobordism ring
Ω^{*} and a complex analogue I, Amer. J.
Math. 82 (1960) 505–521 MR0119209 
36 
J Morava, Forms of
K–theory, Math. Z. 201 (1989) 401–428
MR999737 
37 
J Morava, Complex
cobordism and algebraic topology, arXiv:0707.3216
(2007) 
38 
D Mumford,
Geometric invariant theory, Ergebnisse Series, Springer
(1965) MR0214602 
39 
N Naumann, The stack of
formal groups in stable homotopy theory, Adv. Math. 215
(2007) 569–600 MR2355600 
40 
D Quillen, On the
formal group laws of unoriented and complex cobordism
theory, Bull. Amer. Math. Soc. 75 (1969)
1293–1298 MR0253350 
41 
D C Ravenel,
Complex cobordism and stable homotopy groups of spheres,
Pure and Applied Mathematics 121, Academic Press (1986)
MR860042 
42 
D C Ravenel,
Toward higher chromatic analogs of elliptic cohomology,
from: "Elliptic cohomology", London Math. Soc. Lecture Note
Ser. 342, Cambridge Univ. Press (2007) 286–305 MR2330518 
43 
C Rezk, Notes on
the Hopkins–Miller theorem, from: "Homotopy theory
via algebraic geometry and group representations (Evanston, IL,
1997)", Contemp. Math. 220, Amer. Math. Soc. (1998)
313–366 MR1642902 
44 
C Rezk,
Supplementary notes for Math 512 (2001, url =
http://www.math.uiuc.edu/ rezk/papers.html) 
45 
Y B Rudyak,
Exactness theorems for the cohomology theories MU, BP and
P(n), Mat. Zametki 40 (1986) 115–126, 141 MR864277 
46 
K Shimomura, X
Wang, The homotopy
groups π_{*}(L_{2}S^{0}) at the
prime 3, Topology 41 (2002) 1183–1198 MR1923218 
47 
J H Silverman,
The arithmetic of elliptic curves, Graduate Texts in
Math 106, Springer (1992) MR1329092
Corrected reprint of the 1986 original 
48 
J Tate, Finite flat
group schemes, from: "Modular forms and Fermat's last
theorem (Boston, MA, 1995)", Springer (1997) 121–154
MR1638478 
49 
A Vistoli,
Grothendieck topologies, fibered categories and descent
theory, from: "Fundamental algebraic geometry", Math.
Surveys Monogr. 123, Amer. Math. Soc. (2005) 1–104
MR2223406 
