Geodesic
On Hopkins’ Picard group Pic2 at the prime 3
Karamanov, Nasko1
1Augsburger Strasse 36E, 93051 Regensburg, Germany
Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 275-292
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In this paper we calculate the algebraic Hopkins Picard group Pic2alg at the prime p = 3, which is a subgroup of the group of isomorphism classes of invertible K(2)–local spectra, ie of Hopkins’ Picard group Pic2. We use the resolution of the K(2)–local sphere introduced by Goerss, Henn, Mahowald and Rezk in [Ann. of Math (2) 162 (2005) 777-822] and the methods from Henn, Karamanov and Mahowald [to appear in Math. Zeit. arXiv:0811.0235] and Karamanov [PhD thesis, Universite Louis Pasteur (2006)].

DOI : 10.2140/agt.2010.10.275
Keywords: Hopkins Picard group, Morava $K$–theory, $K(2)$–local sphere

Karamanov, Nasko  1

1 Augsburger Strasse 36E, 93051 Regensburg, Germany 
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Karamanov, Nasko. On Hopkins’ Picard group Pic2 at the prime 3. Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 275-292. doi: 10.2140/agt.2010.10.275

[1] K S Brown, Cohomology of groups, Graduate Texts in Math. 87, Springer (1994)

[2] P Goerss, H W Henn, M Mahowald, The homotopy of $L_2V(1)$ for the prime 3, from: "Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001)" (editors G Arone, J Hubbuck, R Levi, M Weiss), Progr. Math. 215, Birkhäuser (2004) 125

[3] 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

[4] P G Goerss, M J Hopkins, Moduli spaces of commutative ring spectra, from: "Structured ring spectra" (editors A Baker, B Richter), London Math. Soc. Lecture Note Ser. 315, Cambridge Univ. Press (2004) 151

[5] H W Henn, N Karamanov, M Mahowald, The homotopy of the $K(2)$–local Moore spectrum at the prime 3 revisited, to appear in Math. Zeit.

[6] M J Hopkins, M Mahowald, H Sadofsky, Constructions of elements in Picard groups, from: "Topology and representation theory (Evanston, IL, 1992)" (editors E M Friedlander, M E Mahowald), Contemp. Math. 158, Amer. Math. Soc. (1994) 89

[7] N Karamanov, À propos de la cohomologie du deuxième groupe stabilisateur de Morava; application aux calculs de $\pi_{*}{L_{K(2)}V(0)}$ et du groupe $\mathrm{Pic}_2$ de Hopkins, PhD thesis, Université Louis Pasteur (2006)

[8] N P Strickland, On the $p$–adic interpolation of stable homotopy groups, from: "Adams Memorial Symposium on Algebraic Topology, 2 (Manchester, 1990)" (editors N Ray, G Walker), London Math. Soc. Lecture Note Ser. 176, Cambridge Univ. Press (1992) 45

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