# 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}
}
• Published 30 August 2008
• Mathematics
• Nuclear Physics
28 Citations
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of
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## References

SHOWING 1-10 OF 15 REFERENCES

• Mathematics
• 2003
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
• Mathematics
• 2006
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
• Mathematics
• 2005
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
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,
• Mathematics
• 1999
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.
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.
• Art
• 2001
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 ...