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Thom spectra, higher $\mathrm{THH}$ and tensors in $\infty$–categories

Nima Rasekh, Bruno Stonek and Gabriel Valenzuela

Algebraic & Geometric Topology 22 (2022) 1841–1903
Bibliography
1 M Ando, A J Blumberg, D Gepner, Parametrized spectra, multiplicative Thom spectra and the twisted Umkehr map, Geom. Topol. 22 (2018) 3761 MR3890766
2 M Ando, A J Blumberg, D Gepner, M J Hopkins, C Rezk, An –categorical approach to R–line bundles, R–module Thom spectra, and twisted R–homology, J. Topol. 7 (2014) 869 MR3252967
3 V Angeltveit, M A Hill, T Lawson, The spectra ko and ku are not Thom spectra : an approach using THH, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16, Geom. Topol. Publ. (2009) 1 MR2544383
4 O Antolín-Camarena, T Barthel, A simple universal property of Thom ring spectra, J. Topol. 12 (2019) 56 MR3875978
5 S Basu, S Sagave, C Schlichtkrull, Generalized Thom spectra and their topological Hochschild homology, J. Inst. Math. Jussieu 19 (2020) 21 MR4045079
6 A J Blumberg, Topological Hochschild homology of Thom spectra which are E ring spectra, J. Topol. 3 (2010) 535 MR2684512
7 A J Blumberg, R L Cohen, C Schlichtkrull, Topological Hochschild homology of Thom spectra and the free loop space, Geom. Topol. 14 (2010) 1165 MR2651551
8 M Bökstedt, Topological Hochschild homology, unpublished (1985)
9 M Brun, G Carlsson, B I Dundas, Covering homology, Adv. Math. 225 (2010) 3166 MR2729005
10 G Carlsson, C L Douglas, B I Dundas, Higher topological cyclic homology and the Segal conjecture for tori, Adv. Math. 226 (2011) 1823 MR2737802
11 D Clausen, A Mathew, N Naumann, J Noel, Descent in algebraic K–theory and a conjecture of Ausoni–Rognes, J. Eur. Math. Soc. 22 (2020) 1149 MR4071324
12 B Day, A reflection theorem for closed categories, J. Pure Appl. Algebra 2 (1972) 1 MR296126
13 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, 47, Amer. Math. Soc. (1997) MR1417719
14 D Gepner, M Groth, T Nikolaus, Universality of multiplicative infinite loop space machines, Algebr. Geom. Topol. 15 (2015) 3107 MR3450758
15 D Gepner, R Haugseng, Enriched –categories via non-symmetric –operads, Adv. Math. 279 (2015) 575 MR3345192
16 S Glasman, A spectrum-level Hodge filtration on topological Hochschild homology, Selecta Math. 22 (2016) 1583 MR3518559
17 J Hahn, A Yuan, Exotic multiplications on periodic complex bordism, J. Topol. 13 (2020) 1839 MR4186145
18 I Klang, The factorization theory of Thom spectra and twisted nonabelian Poincaré duality, Algebr. Geom. Topol. 18 (2018) 2541 MR3848394
19 N J Kuhn, The McCord model for the tensor product of a space and a commutative ring spectrum, from: "Categorical decomposition techniques in algebraic topology" (editors G Arone, J Hubbuck, R Levi, M Weiss), Progr. Math. 215, Birkhäuser (2004) 213 MR2039768
20 A Lindenstrauss, B Richter, Stability of Loday constructions, Homology Homotopy Appl. 24 (2022) 245 MR4410464
21 J L Loday, Opérations sur l’homologie cyclique des algèbres commutatives, Invent. Math. 96 (1989) 205 MR981743
22 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
23 J Lurie, Derived algebraic geometry, VII: Spectral schemes, preprint (2011)
24 J Lurie, Higher algebra, book project (2017)
25 J Lurie, Elliptic cohomology, II: Orientations, preprint (2018)
26 M Mahowald, Ring spectra which are Thom complexes, Duke Math. J. 46 (1979) 549 MR544245
27 A Mathew, THH and base-change for Galois extensions of ring spectra, Algebr. Geom. Topol. 17 (2017) 693 MR3623668
28 R McCarthy, V Minasian, HKR theorem for smooth S–algebras, J. Pure Appl. Algebra 185 (2003) 239 MR2006429
29 J McClure, R Schwänzl, R Vogt, THH(R)R S1 for E ring spectra, J. Pure Appl. Algebra 121 (1997) 137 MR1473888
30 M C McCord, Classifying spaces and infinite symmetric products, Trans. Amer. Math. Soc. 146 (1969) 273 MR251719
31 H Miller, Finite localizations, Bol. Soc. Mat. Mex. 37 (1992) 383 MR1317588
32 T Nikolaus, P Scholze, On topological cyclic homology, Acta Math. 221 (2018) 203 MR3904731
33 T Pirashvili, Hodge decomposition for higher order Hochschild homology, Ann. Sci. École Norm. Sup. 33 (2000) 151 MR1755114
34 J Rognes, Galois extensions of structured ring spectra and Stably dualizable groups, 898, Amer. Math. Soc. (2008) MR2387923
35 S Sagave, C Schlichtkrull, Virtual vector bundles and graded Thom spectra, Math. Z. 292 (2019) 975 MR3980280
36 C Schlichtkrull, Higher topological Hochschild homology of Thom spectra, J. Topol. 4 (2011) 161 MR2783381
37 V P Snaith, Algebraic cobordism and K–theory, 221, Amer. Math. Soc. (1979) MR539791
38 V Snaith, Localized stable homotopy of some classifying spaces, Math. Proc. Cambridge Philos. Soc. 89 (1981) 325 MR600247
39 B Stonek, Higher topological Hochschild homology of periodic complex K–theory, Topology Appl. 282 (2020) MR4116834
40 R M Switzer, Algebraic topology: homotopy and homology, 212, Springer (1975) MR0385836
41 C A Weibel, S C Geller, Étale descent for Hochschild and cyclic homology, Comment. Math. Helv. 66 (1991) 368 MR1120653
42 C Westerland, A higher chromatic analogue of the image of J, Geom. Topol. 21 (2017) 1033 MR3626597