P-adic analysis (992 bytes)

P-adic number (13914 bytes)

Cohomology (5745 bytes)
1: ...re than does [[homology (mathematics)|homology]]. Cohomology arises from the algebraic dualization of the cons...
3: ...ends to mask the fact that in many applications ''cohomology'', a [[contravariant]] theory, is more natural th...
5: ...nclusive meaning covering both ''homology'' and ''cohomology'': the direction of the arrows in a [[chain compl...
9: ...lity]] theorem, contained the germ of the idea of cohomology, but this was not seen until later.
11: There were various precursors to cohomology. In the mid-[[1920s]], [[ J.W. Alexander]] and [...

Motivic cohomology (1934 bytes)
1: '''Motivic cohomology''' is a homological theory in [[mathematics]], th...
3: ...omology theories in algebraic geometry; the other cohomology theories would be specializations. Progress towar...
7: ...ng category can then be used to produce a motivic cohomology theory for algebraic varieties.

Intersection cohomology (868 bytes)
1: In [[mathematics]], '''intersection cohomology''' is a theory from [[algebraic topology]], initi...
3: The [[cohomology]] groups of a topological [[manifold]] have an in...
7: ...tersection cohomology is a modified definition of cohomology which recovers the property of Poincaré duality f...

Cech cohomology (2935 bytes)
1: ...Čech cohomology''' is a particular type of [[cohomology]] in [[mathematics]]. It is named for the mathema...
9: ...cochain]] [[group (mathematics)|group]]s for this cohomology.
28: ...[[chain complex]] formed we have the '''Čech cohomology of U with values in the presheaf''' ''F''. We wri...
33: then there is a [[well-defined]] map in cohomology
37: this system the '''Čech cohomology of''' ''X'' '''with values in''' ''F''.

Galois cohomology (4377 bytes)
1: ...hat may be derived by more abstract means. Galois cohomology accounts for the way in which taking Galois-invar...
3: ...ogy appeared as the foundational layer of [[étale cohomology]] theory (roughly speaking, the theory as it appl...
5: ...e [[normal basis theorem]] implies that the first cohomology group of the [[additive group]] of ''L'' will van...
11: ...ontrol of a [[local-global principle]] for Galois cohomology. This was formulated by means of results in class...

Cohomology operation (1700 bytes)
1: ...unctor]] defining a [[cohomology theory]], then a cohomology operation should be a [[natural transformation]] ...
6: ... the [[Steenrod square]] operation for [[singular cohomology]], in the case of mod 2 coefficients. The combina...
8: ...n [[extraordinary cohomology theory]] has its own cohomology operations, and these may exhibit a richer set on...

Sheaf cohomology (5522 bytes)
1: ...years after 1950, when it was realised that sheaf cohomology was connected with more classical methods applied...
3: ...cohomology to be defined was that based on [[Cech cohomology]], in which the relatively small change was made ...
5: ...n the failure of the [[long exact sequence]] of [[cohomology group]]s associated to a [[short exact sequence]]...
7: ...inition clarified (at a cost) the status of sheaf cohomology as a [[derived functor]] theory of the global sec...
11: ...roach applied. [[Flat cohomology]], [[crystalline cohomology]] and successors are also applications of the bas...

Cohomology ring (1590 bytes)
1: ... of spaces one obtains a [[ring homomorphism]] on cohomology rings, which is contravariant.
3: Specifically, given a sequence of cohomology groups ''H''^''k''(''X'';''R'') on ''X'...
5: ... gives a multiplication the [[direct sum]] of the cohomology groups
9: The cohomology ring is a [[graded-commutative]] ring in the sens...

De Rham cohomology (3438 bytes)
1: ...[singular homology]], and to [[Alexander-Spanier cohomology]].
22: ...rms modulo exact forms, are called the '''de Rham cohomology groups'''
28: ...or spaces with the [[singular cohomology|singular cohomology group]]s
32: Further, the two cohomology rings are isomorphic (as [[graded ring]]s).
34: ...] is an expression of [[duality]] between de Rham cohomology and the [[homology (mathematics)|homology]] of [[...

Group cohomology (6863 bytes)
3: ...applications to [[group theory]] proper, '''group cohomology''' is a way to study [[group (mathematics)|groups...
12: ...N'') precisely measures the difference. The group cohomology functors ''H''^''n'' in general measure...
19: ...sup>&nbsp;''n''</sup>(''G'',''M''), "the ''n''-th cohomology group of ''G'' with coefficients in ''M''". ''H''...
21: In practice, one often computes the cohomology groups using the following fact: if
27: ...inery of derived functors, we can also define the cohomology groups more concretely, as follows. For ''n''&ge;...

Étale cohomology (7507 bytes)
1: ...rly 1960s. This theory is an example of a [[Weil cohomology theory]] in algebraic geometry, and as such it co...
3: The formal definition of étale cohomology is as the [[derived functor]] of the functor of s...
14: ...es of coefficients can be predicted (via [[Galois cohomology]] and [[Tate module]]s).
18: ...ple in [[SGA4&frac12;]]. On the other hand, étale cohomology quickly found other applications, for example in ...
20: ==l-adic cohomology groups==

Alexander-Spanier cohomology (2140 bytes)
1: ...is similar to and in some sense dual to [[de Rham cohomology]]. It is named for [[J. W. Alexander]] and [[Edwi...
4: Then the ''Alexander-Spanier cohomology groups'' <math>H^k_{\mathrm c}(X)</math> are the ...
25: ...r-Vietoris sequence]] holds for Alexander-Spanier cohomology.

John Tate (2444 bytes)
7: ...llowing decades Tate extended the reach of Galois cohomology: [[Tate-Poitou duality]], [[abelian varieties]], ...
11: ...]. They relate to the Galois action on the l-adic cohomology of an algebraic variety, identifying a space of '...

Non-Archimedean (172 bytes)

Mahler's theorem (1127 bytes)

Pierre Deligne (2692 bytes)
3: ...erre Serre]], leading to important results on the l-adic representations attached to [[modular form]]s, an...
5: ...n particular with [[Lusztig]] on the use of etale cohomology to construct representations of [[algebraic group...
7: ...ga of weights'', uniting [[Hodge theory]] and the l-adic Galois representations. The [[Shimura variety]] t...
13: *[[Deligne cohomology]]

List of homological algebra topics (896 bytes)
32: *[[Group cohomology]]
33: *[[Galois cohomology]]
34: *[[Lie algebra cohomology]]
35: *[[Sheaf cohomology]]

Topological ring (2833 bytes)

<< Prev 20 Result Pages:   1  2  3  4  5  6  7  8  9  10  Next 20 >>