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Journal articles on the topic 'Adams spectral sequence'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Ormsby, Kyle M. "Motivic invariants of p-adic fields." Journal of K-theory 7, no. 3 (2011): 597–618. http://dx.doi.org/10.1017/is011004017jkt153.

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AbstractWe provide a complete analysis of the motivic Adams spectral sequences converging to the bigraded coefficients of the 2-complete algebraic Johnson-Wilson spectra BPGL〈n〉 over p-adic fields. These spectra interpolate between integral motivic cohomology (n = 0), a connective version of algebraic K-theory (n = 1), and the algebraic Brown-Peterson spectrum (n = ∞). We deduce that, over p-adic fields, the 2-complete BPGL〈n〉 splits over 2-complete BPGL〈0〉, implying that the slice spectral sequence for BPGL collapses.This is the first in a series of two papers investigating motivic invariants

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2

Lellmann, Wolfgang, and Mark Mahowald. "The bo-Adams Spectral Sequence." Transactions of the American Mathematical Society 300, no. 2 (1987): 593. http://dx.doi.org/10.2307/2000359.

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3

Dugger, Daniel, and Daniel C. Isaksen. "The motivic Adams spectral sequence." Geometry & Topology 14, no. 2 (2010): 967–1014. http://dx.doi.org/10.2140/gt.2010.14.967.

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4

Burklund, Robert, and Piotr Pstrągowski. "Quivers and the Adams spectral sequence." Advances in Mathematics 471 (June 2025): 110270. https://doi.org/10.1016/j.aim.2025.110270.

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5

Wang, Yuyu, and Jianbo Wang. "The Convergence of Some Products in the Adams Spectral Sequence." MATHEMATICA SCANDINAVICA 117, no. 2 (2015): 304. http://dx.doi.org/10.7146/math.scand.a-22871.

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In this paper, we will use the family of homotopy elements $\zeta_n\in\pi_*S$, represented by $h_0b_n\in \operatorname{Ext}_A^{3,p^{n+1} q+q}(\mathsf{Z}_p, \mathsf{Z}_p)$ in the Adams spectral sequence, to detect a $\zeta_n$-related family $\gamma_{s+3}\beta_2\zeta_{n-1}$ in $\pi_*S$. Our main methods are the Adams spectral sequence and the May spectral sequence, here prime $p\geq 7$, $n>3$, $q=2(p-1)$.

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6

Culver, Dominic Leon, and Paul VanKoughnett. "On the K(1)-local homotopy of $$\mathrm {tmf}\wedge \mathrm {tmf}$$." Journal of Homotopy and Related Structures 16, no. 3 (2021): 367–426. http://dx.doi.org/10.1007/s40062-021-00283-7.

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AbstractAs a step towards understanding the $$\mathrm {tmf}$$ tmf -based Adams spectral sequence, we compute the K(1)-local homotopy of $$\mathrm {tmf}\wedge \mathrm {tmf}$$ tmf ∧ tmf , using a small presentation of $$L_{K(1)}\mathrm {tmf}$$ L K ( 1 ) tmf due to Hopkins. We also describe the K(1)-local $$\mathrm {tmf}$$ tmf -based Adams spectral sequence.

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7

Baker, Andrew, and Andrey Lazarev. "On the Adams spectral sequence forR–modules." Algebraic & Geometric Topology 1, no. 1 (2001): 173–99. http://dx.doi.org/10.2140/agt.2001.1.173.

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8

Mahowald, Mark, and Hal Sadofsky. "$v_n$ telescopes and the Adams spectral sequence." Duke Mathematical Journal 78, no. 1 (1995): 101–29. http://dx.doi.org/10.1215/s0012-7094-95-07806-5.

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9

Lellmann, Wolfgang, and Mark Mahowald. "The $b{\rm o}$-Adams spectral sequence." Transactions of the American Mathematical Society 300, no. 2 (1987): 593. http://dx.doi.org/10.1090/s0002-9947-1987-0876468-1.

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10

Behrens, Mark. "Root invariants in the Adams spectral sequence." Transactions of the American Mathematical Society 358, no. 10 (2005): 4279–341. http://dx.doi.org/10.1090/s0002-9947-05-03773-6.

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11

Hu, P., I. Kriz, and K. Ormsby. "Convergence of the Motivic Adams Spectral Sequence." Journal of K-theory 7, no. 3 (2011): 573–96. http://dx.doi.org/10.1017/is011003012jkt150.

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AbstractWe prove convergence of the motivic Adams spectral sequence to completions at p and η under suitable conditions. We also discuss further conditions under which η can be removed from the statement.

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12

Blanc, David, and Surojit Ghosh. "Mapping algebras and the Adams spectral sequence." Homology, Homotopy and Applications 23, no. 1 (2021): 219–42. http://dx.doi.org/10.4310/hha.2021.v23.n1.a12.

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13

Xiangjun, Wang. "Some notes on the adams spectral sequence." Acta Mathematica Sinica 10, no. 1 (1994): 4–10. http://dx.doi.org/10.1007/bf02561542.

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14

Kato, Ryo, and Katsumi Shimomura. "The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime." Nagoya Mathematical Journal 207 (September 2012): 139–57. http://dx.doi.org/10.1017/s0027763000022339.

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AbstractThe chromatic spectral sequence was introduced by Miller, Ravenel, and Wilson to compute the E2-term of the Adams-Novikov spectral sequence for computing the stable homotopy groups of spheres. The E1-term of the spectral sequence is an Ext group of BP*BP-comodules. There is a sequence of Ext groups for nonnegative integers n with and there are Bockstein spectral sequences computing a module (n – s) from So far, a small number of the E1-terms are determined. Here, we determine the for p > 2 and n > 3 by computing the Bockstein spectral sequence with E1-term for s = 1, 2. As an app

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15

Minami, Norihiko. "The Adams Spectral Sequence and the Triple Transfer." American Journal of Mathematics 117, no. 4 (1995): 965. http://dx.doi.org/10.2307/2374955.

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16

Basu, Samik, David Blanc, and Debasis Sen. "Higher structure in the unstable Adams spectral sequence." Homology, Homotopy and Applications 23, no. 2 (2021): 69–94. http://dx.doi.org/10.4310/hha.2021.v23.n2.a5.

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17

Botvinnik, B. I., and S. O. Kochman. "Adams spectral sequence and higher torsion in $MSp_*$." Publicacions Matemàtiques 40 (January 1, 1996): 157–93. http://dx.doi.org/10.5565/publmat_40196_11.

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18

Mahowald, Mark, and Charles Rezk. "Brown-Comenetz duality and the Adams spectral sequence." American Journal of Mathematics 121, no. 6 (1999): 1153–77. http://dx.doi.org/10.1353/ajm.1999.0043.

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19

Mahowald, Mark, and Paul Shick. "Periodic phenomena in the classical Adams spectral sequence." Transactions of the American Mathematical Society 300, no. 1 (1987): 191. http://dx.doi.org/10.1090/s0002-9947-1987-0871672-0.

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20

Baues, Hans-Joachim, and Mamuka Jibladze. "Secondary derived functors and the Adams spectral sequence." Topology 45, no. 2 (2006): 295–324. http://dx.doi.org/10.1016/j.top.2005.08.001.

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21

Baues, Hans-Joachim, and Martin Frankland. "2-track algebras and the Adams spectral sequence." Journal of Homotopy and Related Structures 11, no. 4 (2016): 679–713. http://dx.doi.org/10.1007/s40062-016-0147-x.

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22

Krueger, Warren M. "The 2-primary K-theory Adams spectral sequence." Journal of Pure and Applied Algebra 36 (1985): 143–58. http://dx.doi.org/10.1016/0022-4049(85)90067-2.

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23

DAVIS, DANIEL G., and TYLER LAWSON. "A DESCENT SPECTRAL SEQUENCE FOR ARBITRARY K(n)-LOCAL SPECTRA WITH EXPLICIT E2-TERM." Glasgow Mathematical Journal 56, no. 2 (2013): 369–80. http://dx.doi.org/10.1017/s001708951300030x.

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AbstractLet n be any positive integer and p be any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with abutment π∗(LK(n)(X)) and E2-term equal to the continuous cohomology of Gn, the extended Morava stabilizer group, with coefficients in a certain discrete Gn-module that is built from various homotopy fixed point spectra of the Morava module of X. This spectral sequence can be contrasted with the K(n)-local En-Adams spectral sequence for π∗(LK(n)(X)), whose E2-term is not known to always be equal to a conti

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24

Greenlees, J. P. C. "Homotopy equivariance, strict equivariance and induction theory." Proceedings of the Edinburgh Mathematical Society 35, no. 3 (1992): 473–92. http://dx.doi.org/10.1017/s0013091500005757.

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An obvious question occurs at the very start of equivariant homotopy theory. What is the relationship between maps equivariant up to homotopy and strictly equivariant maps? This question has been studied by various people, usually away from the group order ([8, 11, 22, 25, 26]). We consider the problem stably and answer it by giving a spectral sequence proceeding from homotopy equivariant to strictly equivariant information. The form of the spectral sequence is not surprising, but there are three distinctive features of our approach: (1) we show that the spectral sequence may be viewed as an A

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25

Belmont, Eva. "Localizing the E2 page of the Adams spectral sequence." Algebraic & Geometric Topology 20, no. 4 (2020): 1965–2028. http://dx.doi.org/10.2140/agt.2020.20.1965.

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26

IWASE, Norio. "CERTAIN MISSING TERMS IN AN UNSTABLE ADAMS SPECTRAL SEQUENCE." Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics 41, no. 2 (1987): 97–113. http://dx.doi.org/10.2206/kyushumfs.41.97.

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27

Cohen, Ralph, Wen Lin, and Mark Mahowald. "The Adams spectral sequence of the real projective spaces." Pacific Journal of Mathematics 134, no. 1 (1988): 27–55. http://dx.doi.org/10.2140/pjm.1988.134.27.

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28

Nakai, Hirofumi, та Douglas C. Ravenel. "On β-elements in the Adams-Novikov spectral sequence". Journal of Topology 2, № 2 (2009): 295–320. http://dx.doi.org/10.1112/jtopol/jtp012.

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29

Liu, Xiugui, and Hao Zhao. "On a product in the classical Adams spectral sequence." Proceedings of the American Mathematical Society 137, no. 07 (2009): 2489–96. http://dx.doi.org/10.1090/s0002-9939-09-09809-8.

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30

Blanc, David A. "Operations on resolutions and the reverse Adams spectral sequence." Transactions of the American Mathematical Society 342, no. 1 (1994): 197–213. http://dx.doi.org/10.1090/s0002-9947-1994-1132432-2.

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31

Davis, Donald M., and Mark Mahowald. "v 1-Periodicity in the unstable adams spectral sequence." Mathematische Zeitschrift 204, no. 1 (1990): 319–39. http://dx.doi.org/10.1007/bf02570877.

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32

Baues, Hans-Joachim, and David Blanc. "Higher order derived functors and the Adams spectral sequence." Journal of Pure and Applied Algebra 219, no. 2 (2015): 199–239. http://dx.doi.org/10.1016/j.jpaa.2014.04.018.

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33

Levine, Marc. "The Adams–Novikov spectral sequence and Voevodsky’s slice tower." Geometry & Topology 19, no. 5 (2015): 2691–740. http://dx.doi.org/10.2140/gt.2015.19.2691.

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34

Lin, Jin Kun. "A pull back theorem in the Adams spectral sequence." Acta Mathematica Sinica, English Series 24, no. 3 (2008): 471–90. http://dx.doi.org/10.1007/s10114-007-1018-5.

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35

Lesh, Kathryn. "The unstable Adams spectral sequence for two-stage towers." Topology and its Applications 101, no. 2 (2000): 161–80. http://dx.doi.org/10.1016/s0166-8641(98)00119-9.

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36

Baues, Hans-Joachim. "Higher order track categories and the algebra of higher order cohomology operations." gmj 17, no. 1 (2010): 25–55. http://dx.doi.org/10.1515/gmj.2010.002.

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Abstract We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an 𝑛-th order track category suitable for studying higher order Toda brackets and the differentials in spectral sequences. We describe various examples of higher order track categories which are topological, in particular the track category of higher cohomology operations. Also, differential algebras give rise to higher order track categories.

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37

Bendersky, Martin, and John R. Hunton. "ON THE COALGEBRAIC RING AND BOUSFIELD–KAN SPECTRAL SEQUENCE FOR A LANDWEBER EXACT SPECTRUM." Proceedings of the Edinburgh Mathematical Society 47, no. 3 (2004): 513–32. http://dx.doi.org/10.1017/s0013091503000518.

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AbstractWe construct a Bousfield–Kan (unstable Adams) spectral sequence based on an arbitrary (and not necessarily connective) ring spectrum $E$ with unit and which is related to the homotopy groups of a certain unstable $E$ completion $X_E^{\wedge}$ of a space $X$. For $E$ an $\mathbb{S}$-algebra this completion agrees with that of the first author and Thompson. We also establish in detail the Hopf algebra structure of the unstable cooperations (the coalgebraic module) $E_*(\underline{E}_*)$ for an arbitrary Landweber exact spectrum $E$, extending work of the second author with Hopkins and wi

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38

Lin, Wen-Hsiung. "Some infinite families in the stable homotopy of spheres." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 3 (1987): 477–85. http://dx.doi.org/10.1017/s0305004100066858.

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39

Shick, Paul. "Odd primary periodic phenomena in the classical Adams spectral sequence." Transactions of the American Mathematical Society 309, no. 1 (1988): 77. http://dx.doi.org/10.1090/s0002-9947-1988-0938921-2.

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40

Beaudry, A., M. Behrens, P. Bhattacharya, D. Culver, and Z. Xu. "On the E2‐term of the bo‐Adams spectral sequence." Journal of Topology 13, no. 1 (2020): 356–415. http://dx.doi.org/10.1112/topo.12136.

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41

González, Jesús. "A vanishing line in the BP〈1〉-Adams spectral sequence." Topology 39, no. 6 (2000): 1137–53. http://dx.doi.org/10.1016/s0040-9383(99)00002-6.

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42

Smirnov, V. A. "Differentials of the Adams spectral sequence and the Kervaire invariant." Doklady Mathematics 80, no. 1 (2009): 573–76. http://dx.doi.org/10.1134/s1064562409040310.

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43

Baker, Andrew. "Hecke Operations and the Adams E2-Term Based on Elliptic Cohomology." Canadian Mathematical Bulletin 42, no. 2 (1999): 129–38. http://dx.doi.org/10.4153/cmb-1999-015-2.

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AbstractHecke operators are used to investigate part of the E2-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of Ext1 which combines use of classical Hecke operators and p-adic Hecke operators due to Serre.

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44

Christensen, J. Daniel, and Martin Frankland. "Higher Toda brackets and the Adams spectral sequence in triangulated categories." Algebraic & Geometric Topology 17, no. 5 (2017): 2687–735. http://dx.doi.org/10.2140/agt.2017.17.2687.

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45

Wang, Guozhen, and Zhouli Xu. "Some extensions in the Adams spectral sequence and the 51–stem." Algebraic & Geometric Topology 18, no. 7 (2018): 3887–906. http://dx.doi.org/10.2140/agt.2018.18.3887.

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46

Shimomura, Katsumi. "On the Adams-Novikov spectral sequence and products of $\beta$-elements." Hiroshima Mathematical Journal 16, no. 1 (1986): 209–24. http://dx.doi.org/10.32917/hmj/1206130547.

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47

Kochman, Stanley O. "A Lambda Complex for the Adams-Novikov Spectral Sequence for Spheres." American Journal of Mathematics 114, no. 5 (1992): 979. http://dx.doi.org/10.2307/2374887.

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48

Ravenel, Douglas C. "Book Review: Manifolds with singularities and the Adams-Novikov spectral sequence." Bulletin of the American Mathematical Society 29, no. 2 (1993): 290–94. http://dx.doi.org/10.1090/s0273-0979-1993-00422-1.

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49

Lawson, Tyler. "Realizability of the Adams-Novikov spectral sequence for formal $A$-modules." Proceedings of the American Mathematical Society 135, no. 3 (2006): 883–90. http://dx.doi.org/10.1090/s0002-9939-06-08521-2.

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50

Isaksen, Daniel C., Hana Jia Kong, Guchuan Li, Yangyang Ruan, and Heyi Zhu. "The C-motivic Adams-Novikov spectral sequence for topological modular forms." Advances in Mathematics 458 (December 2024): 109966. http://dx.doi.org/10.1016/j.aim.2024.109966.

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