Dwork cohomology

General Introduction
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Search results
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Online References
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
Dwork cohomology, de Rham cohomology, and hypergeometric functions. Alan Adolphson, Steven Sperber (Submitted on 3 Oct 1999) In the 1960s, Dwork developed a padic cohomology theory of de Rham type for varieties over finite fields, based on a trace formula for the action of a Frobenius operator on certain spaces of padic analytic functions. One can consider a purely algebraic analogue of Dwork's theory for varieties over a field of characteristic zero and ask what is the connection between this theory and ordinary de Rham cohomology. N. Katz showed that Dwork cohomology coincides with the primitive part of de Rham cohomology for smooth projective hypersurfaces, but the exact relationship for varieties of higher codimension has been an open question. In this article, we settle the case of smooth affine complete intersections.
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