A DG Guide to Voevodsky’s Motives

By A. Beilinson, Vadim Vologodsky. 2006

86 citations recorded by the source corpus.

LetVar be the category ofcom plex algebraic varieties,Top thatofnice topologicalspaces,D ab bethederived category of nitecom plexesof nitely generated abelian groups. One hastensorfunctorsVar ! Top ! D ab,the rstassignsto a variety itsspaceequipped with theclassicaltopology,thesecond oneisthesingularchain com plex functor(thetensorstructureforthe rsttwo categoriesisgiven by the direct product). The basic objective ofthe m otive theory is to llin a com m utativesquare

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7a8b065d62502dc2312e2cc7e98d28bb377296d0

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Citations in the corpus

Singular support of coherent sheaves and the geometric Langlands conjecture (2012, background): “2 we obtain that the short exact sequences TYa1 ⇄ T⇄ TSpec(A)−Ya1 and TYa2 ⇄ T⇄ TSpec(A)−Ya2 are compatible in the sense of [BeVo], Sect.”
On compactly generated torsion pairs and the classification of co--structures for commutative noetherian rings (2012, background): “Bondarko’s motivation [16, 17] stemmed from problems related to Voevodsky’s motives [8].”
Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants (2010, unknown): “he motive of the ind-schemes Muniv γ understood as an element of Voevodsky triangulated category of motives (see [56]). More precisely, we should maybe use a dg enhancement constructed in [10] and in [6]. We expect that the Cohomological Hall algebra has a natural enhancement to an A∞-algebra in the”
Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura (2006, background): “In [3] it was proved unconditionally that DM has a differential graded enhancement.”