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Journal articles on the topic 'Motivic Adams spectral sequence'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 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

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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3

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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4

Isaksen, Daniel C., and Armira Shkembi. "Motivic connective K-theories and the cohomology of A(1)." Journal of K-theory 7, no. 3 (2011): 619–61. http://dx.doi.org/10.1017/is011004009jkt154.

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AbstractWe make some computations in stable motivic homotopy theory over Spec ℂ, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct over ℂ a motivic analogue of the real K-theory spectrum KO. We also establish a theory of motivic connective covers over ℂ to obtain a motivic version of ko. We establish an Adams spectral sequence for computing motivic ko-homology. The E2-term of this spectral sequence involves Ext groups over the subalgebra A(1) of the motivic Steenrod algebra. We make several explicit computations of these E2-terms in interesting speci

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5

Gregersen, Thomas, and John Rognes. "On the motivic Segal conjecture." Journal of Topology 16, no. 3 (2023): 1258–313. http://dx.doi.org/10.1112/topo.12311.

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AbstractWe establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group of th roots of unity, where is any prime. To achieve this we develop motivic Singer constructions associated to the symmetric group and to , and introduce a delayed limit Adams spectral sequence.

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6

Hu, Po, Igor Kriz, and Kyle Ormsby. "Remarks on motivic homotopy theory over algebraically closed fields." Journal of K-Theory 7, no. 1 (2010): 55–89. http://dx.doi.org/10.1017/is010001012jkt098.

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AbstractWe discuss certain calculations in the 2-complete motivic stable homotopy category over an algebraically closed field of characteristic 0. Specifically, we prove the convergence of motivic analogues of the Adams and Adams-Novikov spectral sequences, and as one application, discuss the 2-complete version of the complex motivic J -homomorphism.

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7

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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8

Isaksen, Daniel C., Guozhen Wang, and Zhouli Xu. "Stable homotopy groups of spheres." Proceedings of the National Academy of Sciences 117, no. 40 (2020): 24757–63. http://dx.doi.org/10.1073/pnas.2012335117.

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We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is the

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9

Garkusha, Grigory, and Ivan Panin. "ON THE MOTIVIC SPECTRAL SEQUENCE." Journal of the Institute of Mathematics of Jussieu 17, no. 1 (2015): 137–70. http://dx.doi.org/10.1017/s1474748015000419.

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It is shown that the Grayson tower for $K$-theory of smooth algebraic varieties is isomorphic to the slice tower of $S^{1}$-spectra. We also extend the Grayson tower to bispectra, and show that the Grayson motivic spectral sequence is isomorphic to the motivic spectral sequence produced by the Voevodsky slice tower for the motivic $K$-theory spectrum $\mathit{KGL}$. This solves Suslin’s problem about these two spectral sequences in the affirmative.

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10

Yagunov, Serge. "Motivic cohomology spectral sequence and Steenrod operations." Compositio Mathematica 152, no. 10 (2016): 2113–33. http://dx.doi.org/10.1112/s0010437x16007594.

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For a prime number$p$, we show that differentials$d_{n}$in the motivic cohomology spectral sequence with$p$-local coefficients vanish unless$p-1$divides$n-1$. We obtain an explicit formula for the first non-trivial differential$d_{p}$, expressing it in terms of motivic Steenrod$p$-power operations and Bockstein maps. To this end, we compute the algebra of operations of weight$p-1$with$p$-local coefficients. Finally, we construct examples of varieties having non-trivial differentials$d_{p}$in their motivic cohomology spectral sequences.

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11

Arapura, Donu. "The Leray spectral sequence is motivic." Inventiones mathematicae 160, no. 3 (2004): 567–89. http://dx.doi.org/10.1007/s00222-004-0416-x.

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12

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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13

Yagita, Nobuaki. "Motivic cohomology of quadrics and the coniveau spectral sequence." Journal of K-theory 6, no. 3 (2010): 547–89. http://dx.doi.org/10.1017/is008008012jkt084.

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AbstractWe study the coniveau spectral sequence for quadrics defined by Pfister forms. In particular, we explicitly compute the motivic cohomology of anisotropic quadrics over ℝ, by showing that their coniveau spectral sequences collapse from the -term

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14

Dupont, Clément, and Daniel Juteau. "The localization spectral sequence in the motivic setting." Algebraic & Geometric Topology 24, no. 3 (2024): 1431–66. http://dx.doi.org/10.2140/agt.2024.24.1431.

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15

Krishna, Amalendu, and Pablo Pelaez. "Motivic spectral sequence for relative homotopy K-theory." ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE 21, no. 1 (2020): 411–47. http://dx.doi.org/10.2422/2036-2145.201802_006.

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16

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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17

Shinder, Evgeny. "On the motive of the group of units of a division algebra." Journal of K-theory 13, no. 3 (2014): 533–61. http://dx.doi.org/10.1017/is014003007jkt258.

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AbstractWe consider the algebraic group GL1 (A), where A is a division algebra of prime degree over a field F, and the associated motive in the Voevodsky category of motivic complexes (F). We relate the motive of GL1 (A) to the motive of the Čech simplicial scheme χ, associated to the Severi-Brauer variety of A, and compute the second differential in the resulting spectral sequence for motivic cohomology.

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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

Carrick, Christian, Michael A. Hill, and Douglas C. Ravenel. "The homological slice spectral sequence in motivic and Real bordism." Advances in Mathematics 458 (December 2024): 109955. http://dx.doi.org/10.1016/j.aim.2024.109955.

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27

Friedlander, E. "The spectral sequence relating algebraic K-theory to motivic cohomology." Annales Scientifiques de lʼÉcole Normale Supérieure 35, no. 6 (2002): 773–875. http://dx.doi.org/10.1016/s0012-9593(02)01109-6.

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28

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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29

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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30

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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31

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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32

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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33

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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34

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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35

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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36

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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37

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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38

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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39

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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40

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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41

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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42

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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43

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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44

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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45

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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46

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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47

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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48

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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49

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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50

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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