Grothendieck spectral sequence information

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...

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

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

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

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 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...

{\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)...

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

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

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

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

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

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

proved by Bernard Dwork (1960), the functional equation by Alexander Grothendieck (1965), and the analogue of the Riemann hypothesis by Pierre Deligne (1974)...

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

years; in 1973 Per Enflo gave a counter-example, building on work by Grothendieck and Banach. The origin of the theory of compact operators is in the theory...

topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which has been used in algebraic...