2014
DOI: 10.1007/s00208-014-1158-8
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Integral motives, relative Krull–Schmidt principle, and Maranda-type theorems

Abstract: Abstract. In the present article we investigate properties of the category of the integral Grothendieck-Chow motives over a field.We discuss the Krull-Schmidt principle for integral motives, provide a complete list of the generalized Severi-Brauer varieties with indecomposable integral motive, and exploit a relation between the category of motives of twisted flag varieties and integral p-adic representations of finite groups.

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Cited by 7 publications
(5 citation statements)
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“…Only very few facts are known concerning the subcategory [E/B] of Chow motives with integer coefficients. An integer version of the motive R was introduced and discussed in [31]; in [5], [10], [27] it was shown that [E/B] is not Krull-Schmidt (the uniqueness of a direct sum decomposition fails).…”
Section: Introductionmentioning
confidence: 99%
“…Only very few facts are known concerning the subcategory [E/B] of Chow motives with integer coefficients. An integer version of the motive R was introduced and discussed in [31]; in [5], [10], [27] it was shown that [E/B] is not Krull-Schmidt (the uniqueness of a direct sum decomposition fails).…”
Section: Introductionmentioning
confidence: 99%
“…Motivic decompositions which we considered in this paper were usually with modulo coefficients. Nevertheless, there is a standard technique to lift motivic isomorphisms and motivic decompositions from - to - or -coefficients (see, for example, [SZ15]).…”
Section: Applications To Other Cohomology Theoriesmentioning
confidence: 99%
“…Thus, CH Gfalse(G/Pfalse) CH Tfalse(G/Pfalse) also splits. Remark Since we are mainly interested in motives with double-struckZ‐ or Z/p‐coefficients we could avoid the construction of a splitting of homomorphism using . Namely, it follows from [, Theorem 4.3] that all decompositions of ordinary motives which we consider below hold with Zp‐coefficients in the same way as with Z/p‐coefficients.…”
Section: G‐equivariant Motivesmentioning
confidence: 99%
“…Remark Since we are mainly interested in motives with double-struckZ‐ or Z/p‐coefficients we could avoid the construction of a splitting of homomorphism using . Namely, it follows from [, Theorem 4.3] that all decompositions of ordinary motives which we consider below hold with Zp‐coefficients in the same way as with Z/p‐coefficients. But since Zp is flat over double-struckZ, homomorphism remains injective after tensoring with Zp and this is its only property needed in the proofs below.…”
Section: G‐equivariant Motivesmentioning
confidence: 99%