Geodesic
Modular isogeny complexes
Rezk, Charles1
1Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 W Green Street, Urbana IL 61801, United States
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1373-1403
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We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of power operations for Morava E–theory at height 2.

DOI : 10.2140/agt.2012.12.1373
Classification : 11G18, 55N34, 55S25, 11G15
Keywords: power operations, elliptic curves, Morava E–theory

Rezk, Charles  1

1 Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 W Green Street, Urbana IL 61801, United States 
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Rezk, Charles. Modular isogeny complexes. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1373-1403. doi: 10.2140/agt.2012.12.1373

[1] M H Baker, E González-Jiménez, J González, B Poonen, Finiteness results for modular curves of genus at least 2, Amer. J. Math. 127 (2005) 1325

[2] M Behrens, T Lawson, Isogenies of elliptic curves and the Morava stabilizer group, J. Pure Appl. Algebra 207 (2006) 37

[3] T Kashiwabara, $K(2)$–homology of some infinite loop spaces, Math. Z. 218 (1995) 503

[4] N M Katz, B Mazur, Arithmetic moduli of elliptic curves, Annals of Math. Studies 108, Princeton Univ. Press (1985)

[5] B Poonen (Mathoverflow.Net/Users/2757), Supersingular elliptic curves and their “functorial” structure over $F_p^2$, MathOverflow (2010)

[6] S B Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970) 39

[7] D Quillen, Finite generation of the groups $K^{i}$ of rings of algebraic integers, from: "Algebraic $K$–theory, I: Higher $K$–theories (Proc. Conf., Battelle Memorial Inst., Seattle, WA, 1972)" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 179

[8] C Rezk, Rings of power operations for Morava $E$–theories are Koszul

[9] C Rezk, The congruence criterion for power operations in Morava $E$–theory, Homology, Homotopy Appl. 11 (2009) 327

[10] L Solomon, The Steinberg character of a finite group with $BN$–pair, from: "Theory of Finite Groups (Symposium, Harvard, Cambridge, MA, 1968)", Benjamin (1969) 213

[11] N P Strickland, Finite subgroups of formal groups, J. Pure Appl. Algebra 121 (1997) 161

[12] N P Strickland, Morava $E$–theory of symmetric groups, Topology 37 (1998) 757

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