diff --git a/README.md b/README.md index a3c243d..d75492d 100644 --- a/README.md +++ b/README.md @@ -119,7 +119,7 @@ - [ ] Introduction - [ ] I. Global and local cohomological invariants with respect to a closed subspace 1. [ ] The functors $\Gamma_Z$ and $\underline{\Gamma}_Z$ *(7)* - 2. [ ] The functors $\operatorname{H}_Z^\bullet(X,F)$ and $\underline{\operatorname{H}}_Z^\bullet(F)$ *(6)* + 2. [ ] The functors $\mathop{\text{H}}_Z^\bullet(X,F)$ and $\underline{\mathop{\text{H}}}_Z^\bullet(F)$ *(6)* - [ ] II. Applications to quasi-coherent sheaves on preschemes *(8)* - [ ] III. Cohomological invariants and depth 1. [ ] Reminders *(1)* @@ -131,14 +131,14 @@ 3. [ ] Study of the case where $T$ is left exact and $T(M)$ is of finite type for all $M$ *(3)* 4. [ ] Dualising module. Dualising functor *(5)* 5. [ ] Consequences of the theory of dualising modules *(5)* -- [ ] V. Local duality and structure of the $\operatorname{H}^i(M)$ +- [ ] V. Local duality and structure of the $\\mathop{\text{H}}^i(M)$ 1. [ ] Complexes of homomorphisms *(3)* 2. [ ] The local duality theorem for a local regular ring *(1)* - 3. [ ] Application to the structure of the $\operatorname{H}^i(M)$ *(7)* -- [ ] VI. The functors $\operatorname{Ext}(X;F,G)$ and $\underline{\operatorname{Ext}}(F,G)$ + 3. [ ] Application to the structure of the $\mathop{\text{H}}^i(M)$ *(7)* +- [ ] VI. The functors $\mathop{\text{Ext}}(X;F,G)$ and $\underline{\mathop{\text{Ext}}}(F,G)$ 1. [ ] Generalities *(3)* 2. [ ] Application to quasi-coherent sheaves on preschemes *(2)* -- [ ] VII. Nullity criteria. Coherence conditions for the sheaves $\underline{\operatorname{Ext}}(F,G)$ +- [ ] VII. Nullity criteria. Coherence conditions for the sheaves $\underline{\mathop{\text{Ext}}}(F,G)$ 1. [ ] Study of $i < n$ *(5)* 2. [ ] Study of $i > n$ *(2)* - [ ] VIII. Finiteness theorem @@ -153,8 +153,8 @@ 2. [ ] Comparison of $\mathsf{Et}(Y)$ with $\mathsf{Et}(U)$, for varying 𝑈 *(5)* 3. [ ] Comparison of $\pi_1(X)$ with $\pi_1(U)$ *(7)* - [ ] XI. Applications to the Picard group - 1. [ ] Comparison of $\operatorname{Pic}(\widehat{X})$ with $\operatorname{Pic}(Y)$ *(1)* - 2. [ ] Comparison of $\operatorname{Pic}(Y)$ with $\operatorname{Pic}(U)$, for varying $U$ *(5)* + 1. [ ] Comparison of $\mathop{\text{Pic}}(\widehat{X})$ with $\mathop{\text{Pic}}(Y)$ *(1)* + 2. [ ] Comparison of $\mathop{\text{Pic}}(Y)$ with $\mathop{\text{Pic}}(U)$, for varying $U$ *(5)* 3. [ ] Comparison of $\mathsf{P}(X)$ with $\mathsf{P}(U)$ *(7)* - [ ] XII. Applications to projective algebraic schemes 1. [ ] Projective duality theorem and finiteness theorem *(7)* @@ -190,7 +190,7 @@ 4. [ ] Algebraic structures in the category of preschemes *(15)* 5. [ ] Group cohomology *(6)* - [ ] II. Tangent bundles. Lie algebras - 1. [ ] $\underline{\operatorname{Hom}}_{Z/S}(X,Y)$ functors *(2)* + 1. [ ] $\underline{\mathop{\text{Hom}}}_{Z/S}(X,Y)$ functors *(2)* 2. [ ] The preschemes $I_S(M)$ *(3)* 3. [ ] The tangent bundle, the (E) condition *(11)* 4. [ ] Tangent space of a group. Lie algebras *(15)* @@ -495,7 +495,7 @@ 2. [ ] Pseudo-coherent complexes *(18)* 3. [ ] Link to the classical notion of coherence *(7)* 4. [ ] Perfect complexes *(12)* - 5. [ ] Finite $\operatorname{Tor}$-dimension and perfection *(10)* + 5. [ ] Finite $ \mathop{\text{Tor}}$-dimension and perfection *(10)* 6. [ ] Rank of a perfect complex *(9)* 7. [ ] Duality of perfect complexes *(6)* 8. [ ] Traces and cup-products *(5)*