Computing framed motives
PreprintPreprint, arXiv:2606.22193.
Grigory Garkusha · Swansea University
Publications
Research articles, conference papers, book chapters, and preprints in algebraic geometry, motivic homotopy theory, algebraic K-theory, category theory, topology, homological algebra, ring and module theory.
41
Total publications
2000
Earliest year
2026
Latest year
7
Research areas
Featured Publications
Framed motives, motivic spectra & K-theory
2024
Group schemes and motivic spectra
Israel J. Math. 2023Correspondences and stable homotopy theory
Trans. London Math. Soc. 2023Fibrant resolutions for motivic Thom spectra
Annals of K-theory 2021Framed motives of algebraic varieties (after V. Voevodsky)
J. Amer. Math. Soc. 2019Reconstructing rational stable motivic homotopy theory
Compos. Math. 2016Algebraic Kasparov K-theory. II
Annals of K-theory 2014Algebraic Kasparov K-theory. I
Documenta Math. 2012K-motives of algebraic varieties
Homology Homotopy Appl. 2010Classifying finite localizations of quasi-coherent sheaves
St. Petersburg Math. J. 2007Homotopy theory of associative rings
Advances Math.All Publications
2026 2
The Ziegler spectrum for enriched ringoids and schemes
Conference ProceedingsIn Proc. ECM Satellite Conf. “Functor and Tensor Categories, Models, and Systems” (Santiago de Compostela, 2024), Springer Proceedings in Mathematics & Statistics 521, 2026, pp. 63–98.
2025 2
2024 1
Group schemes and motivic spectra
Journal ArticleIsrael J. Math. 259(2) (2024), 727–758.
2023 5
Correspondences and stable homotopy theory
Journal ArticleTrans. London Math. Soc. 10(1) (2023), 124–155.
Fibrant resolutions for motivic Thom spectra
Journal ArticleAnnals of K-theory 8(3) (2023), 421–488.
Framed motivic Gamma-spaces
Journal ArticleIzv. Math. 87(1) (2023), 1–28.
Semilocal Milnor K-theory
Journal ArticleInt. Math. Research Notices 2023(24), 22069–22095.
Triangulated categories of framed bispectra and framed motives
Journal ArticleSt. Petersburg Math. J. 34(6) (2023), 991–1017.
2022 1
2021 3
Framed motives of relative motivic spheres
Journal ArticleTrans. Amer. Math. Soc. 374(7) (2021), 5131–5161.
Cancellation theorem for framed motives of algebraic varieties
Journal ArticleAdv. Math. 383 (2021), article 107681.
Framed motives of algebraic varieties (after V. Voevodsky)
Journal ArticleJ. Amer. Math. Soc. 34(1) (2021), 261–313.
2020 1
Homotopy invariant presheaves with framed transfers
Journal ArticleCambridge J. Math. 8(1) (2020), 1–94.
2019 2
2018 2
2016 2
2014 2
2013 1
Universal bivariant algebraic K-theories
Journal ArticleJ. Homotopy Relat. Struct. 8(1) (2013), 67–116.
2012 1
K-motives of algebraic varieties
Journal ArticleHomology Homotopy Appl. 14(2) (2012), 211–264.
2010 2
2008 3
Torsion classes of finite type and spectra
Book ChapterIn K-theory and Noncommutative Geometry, European Math. Soc. Publ. House, 2008, pp. 393–412.
Reconstructing projective schemes from Serre subcategories
Journal ArticleJ. Algebra 319(3) (2008), 1132–1153.
Classifying Serre subcategories of finitely presented modules
Journal ArticleProc. Amer. Math. Soc. 136(3) (2008), 761–770.
2007 2
2005 2
2004 3
Injective objects in triangulated categories
Journal ArticleJ. Algebra Appl. 3(4) (2004), 367–389.
Relative homological algebra for the proper class w_f
Journal ArticleComm. Algebra 32(10) (2004), 4043–4072.
A note on almost regular group rings
Journal ArticleJ. Math. Sciences 120(4) (2004), 1561–1562.
2002 3
On the homotopy cofibre spectrum of K(R) → G(R)
Journal ArticleJ. Algebra Appl. 1(3) (2002), 327–334.
Grothendieck categories
Journal ArticleSt. Petersburg Math. J. 13(2) (2002), 149–200.
FP-injective and weakly quasi-Frobenius rings
Journal ArticleJ. Math. Sciences 112(3) (2002), 4303–4312.
2001 1
Grothendieck categories as quotient categories of (R-mod, Ab)
Journal ArticleFund. Appl. Math. 7(4) (2001), 983–992.
2000 1
Duality for categories of finitely presented modules
Journal ArticleSt. Petersburg Math. J. 11(6) (2000), 1051–1061.
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