TY - JOUR
T1 - Dwork cohomology, de Rham cohomology, and hypergeometric functions
AU - Adolphson, Alan
AU - Sperber, Steven
PY - 2000/4
Y1 - 2000/4
N2 - In the 1960s, Dwork developed a p-adic 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 p-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. 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.
AB - In the 1960s, Dwork developed a p-adic 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 p-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. 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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M3 - Article
AN - SCOPUS:0034165050
SN - 0002-9327
VL - 122
SP - 319
EP - 348
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 2
ER -