Algebraic de Rham cohomology

Tags: #subjects/AG #subjects/Physics Refs: https://link.springer.com/content/pdf/10.1007%2F978-3-319-50926-6_3.pdf Links: resolution of singularities

Algebraic de Rham cohomology

References

Closed vs exact: attachments/Pasted%20image%2020220202222055.png

Definitions

attachments/Pasted%20image%2020220315102609.png

attachments/Pasted%20image%2020220209092756.png

Logarithmic

attachments/Pasted%20image%2020220209094009.png Comparison to Crystalline cohomology of the reduction mod \(p\): Frobenius action and Grothendieck-Lefschetz Trace Formula: # Examples

attachments/Pasted%20image%2020220128233100.png

Grothendieck’s Proof

attachments/Pasted%20image%2020220211123817.png

Derivations

attachments/Pasted%20image%2020220213201126.png

Motivations

From physics: attachments/Pasted%20image%2020220213222929.png

Exercises

Affine space:
Elliptic curves:

🗓️ Timeline

2021-09-24

Can you use the Algebraic de Rham cohomology to get a volume form?

Links to this page

unresolved links output

Crystalline cohomology in 2021-04-21, Algebraic de Rham cohomology, arithmetic geometry, perfectoid
period

- Tags: - #subjects/arithmetic-geometry/hodge-theory/p-adic - Refs: - https://home.mathematik.uni-freiburg.de/arithgeom/preprints/friedrich-periods.pdf - Links: - p-adic Hodge theory - Algebraic de Rham
connection

Tags: #subjects/geomtop/differential-geometry Refs: flat connection Milnor fiber Algebraic de Rham
arithmetic geometry

algebraic de Rham cohomology
Weil cohomology

See Algebraic de Rham, crystalline cohomology, l-adic cohomology
Arpon Raksit - Hochschild homology and the derived de Rham complex revisited

The Algebraic de Rham cohomology is used to define derived de Rham cohomology :
900_Changelog

2022-03-15 at 10h26 · Algebraic de Rham cohomology

#subjects/AG #subjects/Physics