Andrei Suslin’s research while affiliated with Northwestern University and other places

... • This is an application of [41] proposition 3.6.5. In particular, given any cartesian square with vertical morphisms isomorphisms and horizontal morphisms closed immersions, noting that the direct image is a functorial assignment, one gets a commutative square ...

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From Six Functors Formalisms to Derived Motivic Measures

... This is a particular case of Theorem 7.1 in [4]. We omit symbol ∼ from the notation when ∼ denotes numerical equivalence ∼ num . ...

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A remark on 0-cycles as modules over algebras of finite correspondences

... This is in contrast to efforts devoted to establish properties of one or more categories of representations of such a finite group scheme. Our techniques do not apply to finite groups, for we utilize the support theory developed in collaboration with A. Suslin and C. Bendel in [22], [23] which replaces cohomological varieties by varieties of 1-parameter subgroups. ...

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Invariants for $\mathbb G_{(r)}$-modules

... Nous renvoyons les lecteurs à [11], [9], [12] pour plus de détails sur la cohomologie non ramifiée. Certains des résultats rappelés ci-dessous (le lemme 6 par exemple) reposent sur la conjecture de Bloch-Kato, étudiée par Merkurjev-Suslin [19], [20], Rost [26] et Voevodsky [29], montrée par Voevodsky [30] et Rost (cf. [28]). ...

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2-Cycles sur les hypersurfaces cubiques de dimension 5

... In the present paper, we slightly adapt the proof from [17] to obtain such a bound, cubic in n, in terms of the Stein-Tits-Vaserstein generators of E(n, R, I), see [15,20,23]. Of course, now we have the advantage of the hindsight, provided by the papers by the second author and Zhang Zuhong, where very similar calculations were performed at the birelative level, see [27,28] and references therein. ...

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Relative Decomposition of Transvections: Explicit Bounds

... On a les propriétés suivantes, conséquences de travaux de Merkurjev et Suslin[20], de A. Suslin[23], de M. Levine[16], de S. Lichtenbaum[18], de B. Kahn[14],[15, Thm. 1.1, Lemme 1.4] ...

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Descente galoisienne sur le second groupe de Chow : mise au point

... Friedlander and Suslin [10] introduced the category of strict polynomial functors of degree d as the representations of the Schur category of degree d, for each non-negative integer d (see Section 4.1). The category of strict polynomial functors of degree d unifies the categories of homogeneous polynomial representations of GL n (F ) of degree d across all n. ...

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Schur Algebras for the Alternating Group and Koszul Duality

... Let k be an algebraically closed field of characteristic p ≥ 2, r ∈ N ≥2 and E r be a p-elementary abelian group of rank r. In [6] and [9] the authors introduced and studied the subcategories of modules with the equal kernels property and the equal images property to get a better understanding of the, in general, wild category mod kE r of finite dimensional kE r -modules. Let x 1 , . . . ...

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Dimension vectors with the equal kernels property

... That is, DM gm B is the compact part and Ind(DM gm B ) = DM B . If k is a field there is a canonical equivalence DM gm B (Spec(k)) = DM gm (k; ‫)ޑ‬ with (the ∞-categorical enhancement of) Voevodsky's category of geometric motives with rational coefficients [48]. ...

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An introduction to six-functor formalisms

... induced by inclusion of the ring R into its fraction field K. So, our results on the conjecture correspond to the case when R is an unramified regular local ring of mixed characteristic and G is the group SL 1 (D) of norm one elements of an Azumaya R-algebra D. The results extend to the mixed characteristic case the ones proved in [23] by A. Suslin and the author. ...

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On Grothendieck-Serre conjecture in mixed characteristic for $\operatorname{SL}_{1,D}