Correction to “Voevodsky’s motives and Weil reciprocity,” Duke Math. J. 162 (2013), 2751–2796

Abstract

We correct a mistake in Section 2.4 of the said paper. In [1, Section 2.4], we wrote: “The category Z Span is isomorphic to the full subcategory of Cor consisting of smooth k-schemes of dimension 0.” Tom Bachmann kindly pointed out to us that this statement is incorrect. Here we clarify the relationship between the two categories and show that it does not affect any argument about cohomological Mackey functors (the only Mackey functors appearing in [1]). We retain the notation of [1]. 1 Let Cor0 be the full subcategory of Cor given by 0-dimensional smooth schemes (D etale k-schemes). If f W X ! Y is a surjective morphism of degree d of etale k-schemes, then we have the formula in Cor0, f i f D d: (1) 2 There is a canonical functor W Z Span!Cor0 (2) which is the identity on objects and sends a span (2.1) from [1], X g Z f ! Y; (3) to f i g. DUKE MATHEMATICAL JOURNAL Vol. 164, No. 10, © 2015 DOI 10.1215/00127094-3146068 Received 23 October 2014. Revision received 14 March 2015. 2010 Mathematics Subject Classification. Primary 19E15; Secondary 19A22, 18D10.