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searching for Quasi-isomorphism 12 found (34 total)

Homotopy Lie algebra (2,645 words) [view diff] exact match in snippet view article find links to article

deformation theory because deformation functors are classified by quasi-isomorphism classes of L ∞ {\displaystyle L_{\infty }} -algebras. This was later

Iwasawa algebra (1,182 words) [view diff] exact match in snippet view article find links to article

modules. The structure of such modules can be described as follows. A quasi-isomorphism of modules is a homomorphism whose kernel and cokernel are both finite

Perfect complex (562 words) [view diff] exact match in snippet view article find links to article

called pseudo-coherent if, for every integer n, there is locally a quasi-isomorphism L → F {\displaystyle L\to F} where L has degree bounded above and

Derived algebraic geometry (1,810 words) [view diff] exact match in snippet view article find links to article

{O}}_{U_{i}}^{\bullet }} would glue on overlaps U i j {\displaystyle U_{ij}} only by quasi-isomorphism. Unfortunately, over characteristic p, differential graded algebras

Homotopy associative algebra (4,777 words) [view diff] exact match in snippet view article find links to article

cohomology algebra H A ∙ {\displaystyle HA^{\bullet }} which preserves the quasi-isomorphism structure of the original differential graded algebra. One common

Coherent duality (1,897 words) [view diff] exact match in snippet view article find links to article

dimension, found in Hartshorne (Residues and duality) is the following quasi-isomorphism R f ∗ R H o m X ( F ∙ , f ! G ∙ ) → R H o m Y ( R f ∗ F ∙ , G ∙ )

Derived scheme (2,276 words) [view diff] exact match in snippet view article find links to article

{\displaystyle A_{\bullet }} differential graded algebra admits a surjective quasi-isomorphism from a semi-free ( A ∙ , d ) {\displaystyle (A_{\bullet },d)} differential

Presheaf with transfers (2,676 words) [view diff] exact match in snippet view article find links to article

open cover This case requires more work, but the end result is a quasi-isomorphism between Z ( 1 ) {\displaystyle \mathbb {Z} (1)} and O ∗ [ − 1 ] {\displaystyle

Koszul complex (5,545 words) [view diff] exact match in snippet view article find links to article

, … , s r ) {\displaystyle K_{s}\to A/(s_{1},\dots ,s_{r})} is a quasi-isomorphism, i.e. H i ⁡ ( K s ) = 0 , i ≠ 0 , {\displaystyle \operatorname

Poisson manifold (12,662 words) [view diff] exact match in snippet view article find links to article

algebraic result, known as the formality conjecture, which involves a quasi-isomorphism of differential graded Lie algebras between the multivector fields

Derived noncommutative algebraic geometry (4,702 words) [view diff] no match in snippet view article find links to article

{O}}(-1)\oplus {\mathcal {O}}(-1)\to {\mathcal {O}}\to 0} giving the quasi isomorphism of O ( − 3 ) {\displaystyle {\mathcal {O}}(-3)} with the complex 0

T-structure (6,305 words) [view diff] exact match in snippet view article find links to article

{A}})} , the cohomology functor H n {\displaystyle H^{n}} is, up to quasi-isomorphism, the usual nth cohomology group of a complex. However, considered