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An overview of abelian varieties in homotopy theory

Tyler Lawson

Geometry & Topology Monographs 16 (2009) 179–214

DOI: 10.2140/gtm.2009.16.179

Bibliography
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 Moret-Bailly, 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*(L2S0) 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