** **dvi file
gen.dvi (needs xy-pic), zipped ps-file gen.ps.zip, pdf-file gen.pdf

Abstract: We prove a generic injectivity
result for etale cohomology which can be formulated as follows.
Theorem: Let W be a connected smooth semi-local scheme over a field k, X --> W a smooth and proper morphism, n an integer prime to char(k) and K a complex of etale sheaves of Z/nZ-modules on X such that the cohomology sheaves are locally constant constructible and bounded below. If w denotes the generic point of W, then for all integers q the natural restriction map of etale hypercohomology groups H^q_et(X, K) --> H^q_et (X_w, K) is a (universal) monomorphism. The result applies to any "extensible pretheory". The proof extends the techniques of section 4 of V. Voevodsky's paper "Cohomological theory of presheaves with transfers" to the relative case. This file differs in two points from the published version. First of all, it doesn't contain the typing error in theorem 1 (full-modules). Secondly, we added the forgotten condition AB5 in the definition of `universal monomorphism' on page 1. (This inaccuracy is already contained in [CHK].) I am grateful to C. Scheiderer who pointed out this mistake to me. |