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The spectrum of Artin motives (2401.02722v2)
Published 5 Jan 2024 in math.AG, math.CT, and math.RT
Abstract: We analyze the tt-geometry of derived Artin motives, via modular representation theory of profinite groups. To illustrate our methods, we discuss Artin motives over a finite field, in which case we also prove stratification.
- Paul Balmer. The spectrum of prime ideals in tensor triangulated categories. J. Reine Angew. Math., 588:149–168, 2005.
- Paul Balmer. Tensor triangular geometry. In Proc. of the International Congress of Mathematicians. Volume II, pages 85–112. Hindustan Book Agency, New Delhi, 2010.
- Paul Balmer. On the surjectivity of the map of spectra associated to a tensor-triangulated functor. Bull. Lond. Math. Soc., 50(3):487–495, 2018.
- Descent in tensor triangular geometry, 2023. Preprint: arXiv:2305.02308.
- Generalized tensor idempotents and the telescope conjecture. Proc. Lond. Math. Soc. (3), 102(6):1161–1185, 2011.
- Permutation modules, Mackey functors, and Artin motives. To appear in Proceedings of ICRA 2020, available at arxiv/2107.11797, preprint 2021.
- Permutation modules and cohomological singularity. Comment. Math. Helv., 97(3):413–430, 2022.
- Three real Artin-Tate motives. Adv. Math., 406: paper no. 108535, 2022.
- Finite permutation resolutions. Duke Math. J., 172(2):201–229, 2023.
- The geometry of permutation modules. Preprint available on authors’ webpages, 2023.
- Stratification in tensor triangular geometry with applications to spectral Mackey functors. Camb. J. Math., 11(4):829–915, 2023.
- Stratifying modular representations of finite groups. Ann. of Math. (2), 174(3):1643–1684, 2011.
- Tensor-triangular fields: ruminations. Selecta Math. (N.S.), 25(1):25:13, 2019.
- Andreas W. M. Dress. Notes on the theory of representations of finite groups. Part I: The Burnside ring of a finite group and some AGN-applications. Universität Bielefeld, Fakultät für Mathematik, Bielefeld, 1971. With the aid of notes by Manfred Küchler.
- Spectral spaces, volume 35 of New Mathematical Monographs. Cambridge University Press, Cambridge, 2019.
- On the Balmer spectrum of Morel-Voevodsky category. Preprint arxiv/2309.09077, 2023.
- Martin Gallauer. Tensor triangular geometry of filtered modules. Algebra Number Theory, 12(8):1975–2003, 2018.
- Martin Gallauer. tt-geometry of Tate motives over algebraically closed fields. Compos. Math., 155(10):1888–1923, 2019.
- Martin Gallauer. A note on Tannakian categories and mixed motives. Bull. Lond. Math. Soc., 53(1):119–129, 2021.
- Wulf-Dieter Geyer. Unendliche algebraische Zahlkörper, über denen jede Gleichung auflösbar von beschränkter Stufe ist. Journal of Number Theory, 1(3):346–374, 1969.
- Primes and fields in stable motivic homotopy theory. Geom. Topol., 22(4):2187–2218, 2018.
- Henning Krause. Decomposing thick subcategories of the stable module category. Math. Ann., 313(1):95–108, 1999.
- Henning Krause. The stable derived category of a Noetherian scheme. Compos. Math., 141(5):1128–1162, 2005.
- 𝐀1superscript𝐀1{\bf A}^{1}bold_A start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT-homotopy theory of schemes. Inst. Hautes Études Sci. Publ. Math., (90):45–143 (2001), 1999.
- Tobias J. Peter. Prime ideals of mixed Artin-Tate motives. Journal of K-Theory, 11(2):331–349, 004 2013.
- Profinite groups, volume 40 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics. Springer-Verlag, Berlin, second edition, 2010.
- Alexander Vishik. Isotropic and numerical equivalence for Chow groups and Morava K-theories. Preprint arxiv/2307.15148, 2023
- Vladimir Voevodsky. Triangulated categories of motives over a field. In Cycles, transfers, and motivic homology theories, volume 143 of Ann. of Math. Stud., pages 188–238. Princeton Univ. Press, Princeton, NJ, 2000.