WebJan 23, 2024 · Deligne cohomology differential K-theory differential elliptic cohomology differential cohomology in a cohesive topos Chern-Weil theory ∞-Chern-Weil theory relative cohomology Extra structure Hodge structure orientation, in generalized cohomology Operations cohomology operations cup product connecting … WebIn this monograph, the authors develop a new theory of p -adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as ...
Periodic Cohomology Theories Defined by Elliptic Curves
WebThis paper is a survey of our mathematical notions of Euclidean eld theories as models for (the cocycles in) a cohomology theory. This subject was pioneered by Graeme Segal [Se1] who suggested more than two decades ago that a cohomology theory known as elliptic cohomology can be described in terms of 2-dimensional (conformal) eld theories. WebAssume khas characteristic 0. Algebraic de Rham cohomology is a Weil cohomology theory with coe cients in K= kon smooth projective varieties over k. We do not assume kalgebraically closed since the most interesting case of this theorem is the case k= Q. We will use the de nition of Weil cohomology theories given in the note on Weil … c8a キシレン
The "need" for cohomology theories - Mathematics Stack Exchange
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a … See more Singular cohomology is a powerful invariant in topology, associating a graded-commutative ring with any topological space. Every continuous map f: X → Y determines a homomorphism from the cohomology ring of … See more In what follows, cohomology is taken with coefficients in the integers Z, unless stated otherwise. • The … See more Another interpretation of Poincaré duality is that the cohomology ring of a closed oriented manifold is self-dual in a strong sense. Namely, let X be a closed connected oriented … See more For each abelian group A and natural number j, there is a space $${\displaystyle K(A,j)}$$ whose j-th homotopy group is isomorphic to A and whose other homotopy groups … See more The cup product on cohomology can be viewed as coming from the diagonal map Δ: X → X × X, x ↦ (x,x). Namely, for any spaces X and Y … See more An oriented real vector bundle E of rank r over a topological space X determines a cohomology class on X, the Euler class χ(E) ∈ H (X,Z). Informally, the Euler class is the class of the zero set of a general section of E. That interpretation can be made more explicit … See more For any topological space X, the cap product is a bilinear map for any integers i … See more WebJan 16, 2024 · cobordism cohomology theory integral cohomology K-theory elliptic cohomology, tmf taf abelian sheaf cohomology Deligne cohomology de Rham cohomology Dolbeault cohomology etale cohomology group of units, Picard group, Brauer group crystalline cohomology syntomic cohomology motivic cohomology … WebCohomology Theories Edgar H. Brown, Jr. The Annals of Mathematics, 2nd Ser., Vol. 75, No. 3. (May, 1962), pp. 467-484. Stable URL: http://links.jstor.org/sici?sici=0003 … c89とは