Relevant bibliographies by topics / Motivic Adams spectral sequence

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  2. Dissertations / Theses
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Academic literature on the topic 'Motivic Adams spectral sequence'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Motivic Adams spectral sequence"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Motivic Adams spectral sequence"

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Andrews, Michael Joseph Ph D. Massachusetts Institute of Technology. "The v₁-periodic part of the Adams spectral sequence at an odd prime/." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99328.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.<br>In title on title-page, "v" is italicized, and "1" is subscript. Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 139-140).<br>We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the "dancers to a discordant system." We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence for the odd primary Adams E₂-page. Furthermore,
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2

Petrovic, Vojislav. "The K(n)-local E n-Adams Spectral Sequence and a Cohomological Approximation of its E2-term." Thesis, University of Louisiana at Lafayette, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10623147.

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<p> Let <i>n</i> &ge; 1 be any integer and let <i>p</i> be a prime number. For a profinite group <i>G</i> and any discrete abelian group <i>M</i>, we use Map<sup>c</sup>(<i>G, M </i>) to denote the abelian group of continuous functions from <i> G</i> to <i>M</i>. For the most part, our interests lie in a particular profinite group known as the extended Morava stabilizer group. Denoted by <i>G<sub>n</sub></i>, this profinite group is the semi-direct product of the Morava stabilizer group Sn with the Galois group of the field extension <b>F</b><i><sub>p<sup>n</sup></sub></i>/<b> F</b><i><sub>p</
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Behrens, Mark. "Root invariants in the Adams spectral sequence /." 2003. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3088714.

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Kan, Chung-Wei, and 甘崇瑋. "The differential in the Adams spectral sequence for spheres." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/64596022888616182984.

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博士<br>國立清華大學<br>數學系<br>89<br>The differential in the Adams spectral sequence for spheres Let A denote the mod 2 Steenrod algebra . The mod 2 Adams spectral sequence is one of the most important tools for computing the 2-adic stable homotopy groups of spheres , which has E_2 term =Ext group , the cohomology of the mod 2 Steenrod algebra . Let h{i} be the class corresponding to the generator sq{2^{i}}in A as described by J. F. Adams in [ 1] . Adams also proves that h{i}^{2} in Ext group and that h{i}^{3}=h{i-1}^{2}h{i+1} in Ext group for all i>=0 . It is well known that h{
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Books on the topic "Motivic Adams spectral sequence"

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Rognes, John, and Robert R. Bruner. Adams Spectral Sequence for Topological Modular Forms. American Mathematical Society, 2022.

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Adams Spectral Sequence for Topological Modular Forms. American Mathematical Society, 2021.

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3

Manifolds with singularities and the Adams-Novikov spectral sequence. Cambridge University Press, 1992.

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4

Botvinnik, Boris I. Manifolds with Singularities and the Adams-Novikov Spectral Sequence. Cambridge University Press, 2011.

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Botvinnik, Boris I. Manifolds with Singularities and the Adams-Novikov Spectral Sequence. Cambridge University Press, 2010.

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Book chapters on the topic "Motivic Adams spectral sequence"

1

Grayson, Daniel R. "The Motivic Spectral Sequence." In Handbook of K-Theory. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-27855-9_2.

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Fomenko, Anatoly, and Dmitry Fuchs. "Chapter 5: The Adams Spectral Sequence." In Graduate Texts in Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-23488-5_5.

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Switzer, Robert M. "The Adams Spectral Sequence and the e-Invariant." In Algebraic Topology — Homotopy and Homology. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-61923-6_20.

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Bruner, Robert R. "The adams spectral sequence of H∞ ring spectra." In H∞ Ring Spectra and their Applications. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075411.

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Merkurjev, Alexander. "Adams Operations and the Brown-Gersten-Quillen Spectral Sequence." In Quadratic Forms, Linear Algebraic Groups, and Cohomology. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6211-9_19.

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Brown, Edgar H., and Ralph L. Cohen. "IV. The Adams Spectral Sequence of Ω2S3 and Brown Gitlet Spectra." In Algebraic Topology and Algebraic K-Theory (AM-113), edited by William Browder. Princeton University Press, 1988. http://dx.doi.org/10.1515/9781400882113-005.

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7

Davis, Donald M. "The bo-adams spectral sequence: Some calculations and a proof of its vanishing line." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078745.

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"The Adams Spectral Sequence." In A User's Guide to Spectral Sequences. Cambridge University Press, 2000. http://dx.doi.org/10.1017/cbo9780511626289.012.

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"The Adams-Novikov spectral sequence." In Manifolds with Singularities and the Adams-Novikov Spectral Sequence. Cambridge University Press, 1992. http://dx.doi.org/10.1017/cbo9780511662645.005.

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10

Barnes, Dianne, David Poduska, and Paul Shick. "Unstable Adams spectral sequence charts." In Adams Memorial Symposium on Algebraic Topology. Cambridge University Press, 1992. http://dx.doi.org/10.1017/cbo9780511526312.013.

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