homological algebra, the Grothendieck spectral sequence, introduced by Alexander Grothendieck in his Tôhoku paper, is a spectral sequence that computes the derived...

example, for the spectral sequence of a filtered complex, described below, r0 = 0, but for the Grothendieck spectral sequence, r0 = 2. Usually r0 is zero...

Leray. It is usually seen nowadays as a special case of the Grothendieck spectral sequence. Let f : X → Y {\displaystyle f:X\to Y} be a continuous map...

{\text{coinf}} H_{1}(G/N,A_{N})\to 0.} The spectral sequence is an instance of the more general Grothendieck spectral sequence of the composition of two derived...

that every Grothendieck category is a quotient category of a module category. The Tôhoku paper also introduced the Grothendieck spectral sequence associated...

spectral sequence Grothendieck–Springer resolution Grothendieck–Teichmüller group Grothendieck–Teichmüller theory Grothendieck-Witt ring Grothendieck...

a variety X over a field k, the second spectral sequence from above gives the Hodge–de Rham spectral sequence for algebraic de Rham cohomology: E 1 p...

In mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed...

topological spaces, and other "tangible" mathematical objects. A spectral sequence is a powerful tool for this. It has played an enormous role in algebraic...

completely faithfully) by complicated spectral sequences. The development of the derived category, by Alexander Grothendieck and his student Jean-Louis Verdier...

exact sequence 0 → E ′ → E → E ″ → 0. {\displaystyle 0\to {\mathcal {E}}'\to {\mathcal {E}}\to {\mathcal {E}}''\to 0.} This gives the Grothendieck-group...

{\displaystyle R^{r}f_{*}\to R^{r}f_{*}\circ g'_{*}\circ g'^{*}.} The Grothendieck spectral sequence then gives the first map and the last map (they are edge maps)...

In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets...

For sheaf cohomology on an algebraic variety, Alexander Grothendieck found six spectral sequences relating the possible hyperhomology groups of two chain...

relations Serre subcategory Serre functor Serre spectral sequence Lyndon–Hochschild–Serre spectral sequence Serre–Swan theorem Serre–Tate theorem Serre's...

Mayer–Vietoris spectral sequence) in the case where the open cover used to compute the Čech cohomology consists of two open sets. This spectral sequence exists...

the Grothendieck group of coherent sheaves and the Chow ring of a smooth projective variety X {\displaystyle X} . Atiyah–Hirzebruch spectral sequence (computational...

the study of sheaf cohomology is Grothendieck's 1957 Tôhoku paper. Sheaves, sheaf cohomology, and spectral sequences were introduced by Jean Leray at...

big theorem in this space is the Hodge decomposition found using a spectral sequence associated to sheaf cohomology groups, proved by Deligne. Essentially...

for each short exact sequence of vector bundles: 0 → V ′ → V → V ″ → 0 , {\displaystyle 0\to V'\to V\to V''\to 0,} Grothendieck imposed the relation [V]...

groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures. Étale cohomology theory can be...

critères de dégénérescence de suites spectrales (Theorem of Lefschetz and criteria of degeneration of spectral sequences). He completed his doctorate at the...

therefore serve for computational purposes, for example the Leray spectral sequence. An injective sheaf F {\displaystyle {\mathcal {F}}} is a sheaf that...

Snapper, Ernst (1964). "Cohomology of Permutation Representations1 I. Spectral Sequences". Journal of Mathematics and Mechanics. 13 (1): 133–161. JSTOR 24901188...

of p {\displaystyle p} ). In this theorem, which is due to Alexander Grothendieck, it is crucial that the vector space V {\displaystyle V} be a subset...

homological algebra techniques. Serre's thesis concerned the Leray–Serre spectral sequence associated to a fibration. Together with Cartan, Serre established...

Commutative diagram Exact sequence Five lemma Short five lemma Snake lemma Splitting lemma Extension problem Spectral sequence Abelian category Group cohomology...

spectral sequence from motivic cohomology to algebraic K-theory for every smooth scheme X over a field, analogous to the Atiyah-Hirzebruch spectral sequence...

younger newcomers including Jean-Pierre Serre and Alexander Grothendieck. Serre, Grothendieck and Laurent Schwartz were awarded the Fields Medal during...

theorem Whitehead theorem Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional...