scholarly journals Intermediate extension of Chow motives of Abelian type

2017 ◽  
Vol 305 ◽  
pp. 515-600 ◽  
Author(s):  
Jörg Wildeshaus
Keyword(s):  
Chow Motives

scholarly journals ℤ[1/p]-motivic resolution of singularities

2011 ◽  
Vol 147 (5) ◽  
pp. 1434-1446 ◽  
Author(s):  
M. V. Bondarko
Keyword(s):  
Preceding Paper ◽  
Resolution Of Singularities ◽  
Cohomology Theory ◽  
Spectral Sequences ◽  
Perfect Field ◽  
Chow Motives ◽  
Unramified Cohomology ◽  
Weight Structure ◽  
Weight Structures

AbstractThe main goal of this paper is to deduce (from a recent resolution of singularities result of Gabber) the following fact: (effective) Chow motives with ℤ[1/p]-coefficients over a perfect field k of characteristic p generate the category DMeffgm[1/p] (of effective geometric Voevodsky’s motives with ℤ[1/p]-coefficients). It follows that DMeffgm[1/p] can be endowed with a Chow weight structure wChow whose heart is Choweff[1/p] (weight structures were introduced in a preceding paper, where the existence of wChow for DMeffgmℚ was also proved). As shown in previous papers, this statement immediately yields the existence of a conservative weight complex functor DMeffgm[1/p]→Kb (Choweff [1/p]) (which induces an isomorphism on K0-groups), as well as the existence of canonical and functorial (Chow)-weight spectral sequences and weight filtrations for any cohomology theory on DMeffgm[1/p] . We also mention a certain Chow t-structure for DMeff−[1/p] and relate it with unramified cohomology.

scholarly journals The Chow Motives of Relative Fulton-Macpherson Space

2013 ◽  
Vol 113 (1) ◽  
pp. 20
Author(s):  
Fumitoshi Sato
Keyword(s):  
Projective Variety ◽  
Chow Groups ◽  
Configuration Spaces ◽  
Chow Motives

Suppose that $X$ is a complex nonsingular projective variety and $D$ is a smooth divisor. Compactifications of configuration spaces of distinct and non-distinct $n$ points in $X$ away from $D$ were constructed by the author and B. Kim in "A generalization of Fulton-MacPherson configuration spaces" by using the method of wonderful compactification. In this paper, we give explicit presentations of Chow motives and Chow groups of these configuration spaces.

scholarly journals Functoriality of motivic lifts of the canonical construction

2019 ◽  
Vol 163 (1-2) ◽  
pp. 27-56 ◽  
Author(s):  
Alex Torzewski
Keyword(s):  
Full Subcategory ◽  
Hodge Structure ◽  
Compact Subgroup ◽  
Base Change ◽  
Shimura Varieties ◽  
Open Compact Subgroup ◽  
Chow Motives ◽  
Variation Of Hodge Structure

Abstract Let $$(G,{\mathfrak {X}})$$ ( G , X ) be a Shimura datum and K a neat open compact subgroup of $$G(\mathbb {A}_f)$$ G ( A f ) . Under mild hypothesis on $$(G,{\mathfrak {X}})$$ ( G , X ) , the canonical construction associates a variation of Hodge structure on $$\text {Sh}_K(G,{\mathfrak {X}})(\mathbb {C})$$ Sh K ( G , X ) ( C ) to a representation of G. It is conjectured that this should be of motivic origin. Specifically, there should be a lift of the canonical construction which takes values in relative Chow motives over $$\text {Sh}_K(G,{\mathfrak {X}})$$ Sh K ( G , X ) and is functorial in $$(G,{\mathfrak {X}})$$ ( G , X ) . Using the formalism of mixed Shimura varieties, we show that such a motivic lift exists on the full subcategory of representations of Hodge type $$\{(-1,0),(0,-1)\}$$ { ( - 1 , 0 ) , ( 0 , - 1 ) } . If $$(G,{\mathfrak {X}})$$ ( G , X ) is equipped with a choice of PEL-datum, Ancona has defined a motivic lift for all representations of G. We show that this is independent of the choice of PEL-datum and give criteria for it to be compatible with base change. Additionally, we provide a classification of Shimura data of PEL-type and demonstrate that the canonical construction is applicable in this context.

scholarly journals Chow motives of abelian type over a base

2018 ◽  
Vol 4 (3) ◽  
pp. 1065-1086
Author(s):  
Vladimir Guletskiĭ
Keyword(s):  
Chow Motives

scholarly journals Relative Equivariant Motives and Modules

2019 ◽  
pp. 1-29
Author(s):  
Baptiste Calmès ◽  
Alexander Neshitov ◽  
Kirill Zainoulline
Keyword(s):  
Generic Version ◽  
Flag Variety ◽  
Flag Varieties ◽  
Direct Sum ◽  
Chow Motives ◽  
Direct Sum Decomposition ◽  
Oriented Cohomology ◽  
Demazure Modules ◽  
Algebraic Cobordism

Abstract We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag variety depends on the direct sum decomposition type of the parabolic module. To do this we use localization techniques of Kostant and Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties.

scholarly journals Derived equivalent threefolds, algebraic representatives, and the coniveau filtration

2018 ◽  
Vol 167 (01) ◽  
pp. 123-131 ◽  
Author(s):  
JEFFREY D. ACHTER ◽  
SEBASTIAN CASALAINA-MARTIN ◽  
CHARLES VIAL
Keyword(s):  
Abelian Varieties ◽  
Projective Varieties ◽  
Chow Motives ◽  
Smooth Projective Varieties ◽  
Coniveau Filtration

AbstractA conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field have isomorphic Chow motives. The conjecture is known for curves, and was recently observed for surfaces by Huybrechts. In this paper we focus on threefolds over perfect fields, and unconditionally secure results, which are implied by Orlov's conjecture, concerning the geometric coniveau filtration, and abelian varieties attached to smooth projective varieties.

scholarly journals A GOING DOWN THEOREM FOR GROTHENDIECK CHOW MOTIVES

2012 ◽  
Vol 64 (3) ◽  
pp. 721-728
Author(s):  
C. de Clercq
Keyword(s):  
Chow Motives
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