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Spanier-Whitehead Duality in Etale Homotopy

Roy Joshua
Transactions of the American Mathematical Society
Vol. 296, No. 1 (Jul., 1986), pp. 151-166
DOI: 10.2307/2000566
Stable URL: http://www.jstor.org/stable/2000566
Page Count: 16
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Spanier-Whitehead Duality in Etale Homotopy
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Abstract

We construct a (mod-l) Spanier-Whitehead dual for the etale homotopy type of any geometrically unibranched and projective variety over an algebraically closed field of arbitrary characteristic. The Thom space of the normal bundle to imbedding any compact complex manifold in a large sphere as a real submanifold provides a Spanier-Whitehead dual for the disjoint union of the manifold and a base point. Our construction generalises this to any characteristic. We also observe various consequences of the existence of a mod-l) Spanier-Whitehead dual.

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