Holmstrom de Rham cohomology

de Rham cohomology

Cycle class map. See section 6 of Esnault and Viehweg


de Rham cohomology

There are several different things called de Rham cohomology.

Most importantly, algebraic geometry and differential geometry.

It can also be defined for D-modules.


de Rham cohomology

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de Rham cohomology

AG (Algebraic geometry), GM (Other, not algebraic, areas of geometry), AT (Algebraic topology)

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de Rham cohomology

Should perhaps refer to Algebraic de Rham cohomology for the Algebraic Geometry world.

Grothendieck: On the de Rham cohomology of algebraic varieties. (Pub. Math. I.H.E.S)

Hartshorne: Algebraic de Rham cohomology

Ernst-Ulrich Gekeler, de Rham cohomology for Drinfel\cprime d modules (pp.\ 57–85) (1990)

Dupont: Simplicial de Rham cohomology and characteristic classes of flat bundles (1976)

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de Rham cohomology

Pure

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de Rham cohomology

See also Algebraic de Rham cohomology


de Rham cohomology

From calculus to cohomology.

Bott and Tu.

MR1807281 (2002h:14031) 14F40 (12H20 14F30 14G22 32C38) Andr´e,Yves Andr´e, Yves1; Baldassarri, Francesco (I-PADV-PM) FDe Rhamcohomology of differential modules on algebraic varieties. See the long review, I don’t have the book.

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de Rham cohomology

Integral structure relevant for zeta values!

arXiv:0909.1849 Canonical extensions of Néron models of Jacobians from arXiv Front: math.NT by Bryden Cais Let A be the Néron model of an abelian variety A_K over the fraction field K of a discrete valuation ring R. Due to work of Mazur-Messing, there is a functorial way to prolong the universal extension of A_K by a vector group to a smooth and separated group scheme over R, called the canonical extension of A. In this paper, we study the canonical extension when A_K=J_K is the Jacobian of a smooth proper and geometrically connected curve X_K over K. Assuming that X_K admits a proper flat regular model X over R that has generically smooth closed fiber, our main result identifies the identity component of the canonical extension with a certain functor Pic^{\natural,0}_{X/R} classifying line bundles on X that have partial degree zero on all components of geometric fibers and are equipped with a regular connection. This result is a natural extension of a theorem of Raynaud, which identifies the identity component of the Néron model J of J_K with the functor Pic^0_{X/R}. As an application of our result, we prove a comparison isomorphism between two canonical integral structures on the de Rham cohomology of X_K.


de Rham cohomology

http://mathoverflow.net/questions/52322/de-rham-cohomology-of-formal-groups

nLab page on de Rham cohomology

Created on June 10, 2014 at 21:14:54 by Andreas Holmström