Twisted de Rham cohomology, homological definition of the integral and “Physics over a ring”

@article{Schwarz2008TwistedDR,
  title={Twisted de Rham cohomology, homological definition of the integral and “Physics over a ring”},
  author={Albert S. Schwarz and Ilya L. Shapiro},
  journal={Nuclear Physics},
  year={2008},
  volume={809},
  pages={547-560}
}

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References

SHOWING 1-10 OF 15 REFERENCES

On Dwork cohomology and algebraic D-modules

After works by Katz, Monsky, and Adolphson-Sperber, a comparison theorem between relative de Rham cohomology and Dwork cohomology is established in a paper by Dimca-Maaref-Sabbah-Saito in the

Supergeometry and Arithmetic Geometry

Electric-Magnetic Duality And The Geometric Langlands Program

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are

Nonabelian Hodge theory in characteristic p

Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use

Algebraic D-modules

Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent,

Dwork Cohomology and Algebraic D-Modules

Using local cohomology and algebraic D-Modules, we generalize a comparison theorem between relative de Rham cohomology and Dwork cohomology due to N. Katz, A. Adolphson and S. Sperber.

On a twisted de Rham complex, II

We prove an algebraic formula, conjectured by M. Kontsevich, for computing the monodromy of the vanishing cycles of a regular function on a smooth complex algebraic variety.

Mathematics Unlimited: 2001 and Beyond

This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we ...