Rendiconti del Seminario Matematico della Università di Padova

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Volume 135, 2016, pp. 223–250
DOI: 10.4171/RSMUP/135-13

Proper base change for separated locally proper maps

Olaf M. Schnürer[1] and Wolfgang Soergel[2]

(1) Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany
(2) Mathematisches Institut, Universität Freiburg, Eckerstraße 1, 79104, Freiburg i. Br., Germany

We introduce and study the notion of a locally proper map between topological spaces.We show that fundamental constructions of sheaf theory, more precisely proper base change, projection formula, and Verdier duality, can be extended from continuous maps between locally compact Hausdor spaces to separated locally proper maps between arbitrary topological spaces.

Keywords: Locally proper map, proper direct image, proper base change, Verdier duality, six operations

Schnürer Olaf, Soergel Wolfgang: Proper base change for separated locally proper maps. Rend. Sem. Mat. Univ. Padova 135 (2016), 223-250. doi: 10.4171/RSMUP/135-13