Three real Artin-Tate motives

Balmer, Paul; Gallauer, Martin

doi:10.1016/j.aim.2022.108535

Cited by 3 publications

(1 citation statement)

References 31 publications

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“…This substantially improves our understanding of the spectrum. Balmer and Gallauer managed to completely describe the spectra of the subcategories of Tate and Artin-Tate motives in the Voevodsky category in [5] and [10] for special fields, but very little was known about Spc(DM (k) c ) itself, in general. Our results show, in particular, that this Balmer spectrum is pretty large.…”

Section: Introductionmentioning

confidence: 99%

On isotropic and numerical equivalence of cycles

Vishik

2022

Sel. Math. New Ser.

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We study the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with $$\mathbb {F}_p$$ F p -coefficients). This conjecture is essential for understanding the structure of the isotropic motivic category and that of the tensor triangulated spectrum of Voevodsky category of motives. We prove the conjecture for the new range of cases. In particular, we show that, for a given variety X, it holds for sufficiently large primes p. We also prove the p-adic analogue. This permits to interpret integral numerically trivial classes in $${\text {CH}}(X)$$ CH ( X ) as $$p^{\infty }$$ p ∞ -anisotropic ones.

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Section: Introductionmentioning

confidence: 99%

On isotropic and numerical equivalence of cycles

Vishik

2022

Sel. Math. New Ser.

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Isotropic and numerical equivalence for Chow groups and Morava K-theories

Vishik

2024

Invent. math.

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In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with ${\Bbb {F}}_{p}$ F p -coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In particular, homs between such objects are finite groups and ⊗ has no zero-divisors. It provides a large supply of new points for the Balmer spectrum of the Voevodsky motivic category. We also prove the Morava K-theory version of the above result, which permits to construct plenty of new points for the Balmer spectrum of the Morel-Voevodsky ${\mathbb{A}}^{1}$ A 1 -stable homotopy category. This substantially improves our understanding of the mentioned spectra whose description is a major open problem.

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