pairing H r ( X , F ) × Ext 3 − r ⁡ ( F , G m ) → H 3 ( X , G m ) = Q / Z {\displaystyle H^{r}(X,F)\times \operatorname {Ext} ^{3-r}(F,\mathbb {G} _{m})\to...

algorithmic perspective. Texts in Theoretical Computer Science (2nd rev. and ext. ed.). Springer. ISBN 978-3-540-43466-5. Zbl 1055.68058. Cantor, G. (1874)...

codimension 2 subvarieties Y {\displaystyle Y} using a certain Ext 1 {\displaystyle {\text{Ext}}^{1}} -group calculated on X {\displaystyle X} . This is given...

1991 he held a research professorship at the Max-Planck-Institut für Mathematik in Bonn. In 1991 he became a full professor at the University of Cologne...

each equation and the vanishing of a derived functor E x t 1 {\displaystyle Ext^{1}} . Let n ≤ m {\displaystyle n\leq m} . Set Y = { x 1 = ⋯ = x n } {\displaystyle...

an associated algebra, called its Ext algebra, defined as Ext A ∙ ⁡ ( k A , k A ) {\displaystyle \operatorname {Ext} _{A}^{\bullet }(k_{A},k_{A})} , where...

0} which represents a non-zero element v ∈ Ext 1 ( O ( 1 ) , O ( − 1 ) ) ≅ k {\displaystyle v\in {\text{Ext}}^{1}({\mathcal {O}}(1),{\mathcal {O}}(-1))\cong...

{F} _{\mathrm {rad} }+\mathbf {F} _{\mathrm {ext} }=mt_{0}{\ddot {\mathbf {v} }}+\mathbf {F} _{\mathrm {ext} }.} where t 0 = μ 0 q 2 6 π m c . {\displaystyle...

Injective resolutions can be used to define derived functors such as the Ext functor. The length of a finite injective resolution is the first index n...

deformation space of an object E is Ext X 1 ⁡ ( E , E ) ≅ Hom ⁡ ( E , E [ 1 ] ) {\displaystyle \operatorname {Ext} _{X}^{1}(E,E)\cong \operatorname {Hom}...