Universität zu Köln

Alldridge, Alexander ORCID: 0000-0001-6331-1672, Hilgert, Joachim and Wurzbacher, Tilmann (2014). Singular superspaces. Math. Z., 278 (1-2). S. 441 - 493. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1823

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Abstract

We introduce a wide category of superspaces, called locally finitely generated, which properly includes supermanifolds, but enjoys much stronger permanence properties, as are prompted by applications. Namely, it is closed under taking finite fibre products (i.e. is finitely complete) and thickenings by spectra of Weil superalgebras. Nevertheless, in this category, morphisms with values in a supermanifold are still given in terms of coordinates. This framework gives a natural notion of relative supermanifolds over a locally finitely generated base. Moreover, the existence of inner homs, whose source is the spectrum of a Weil superalgebra, is established; they are generalisations of the Weil functors defined for smooth manifolds.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Alldridge, Alexander UNSPECIFIED orcid.org/0000-0001-6331-1672 UNSPECIFIED Hilgert, Joachim UNSPECIFIED UNSPECIFIED UNSPECIFIED Wurzbacher, Tilmann UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-427172
DOI:	10.1007/s00209-014-1323-5
Journal or Publication Title:	Math. Z.
Volume:	278
Number:	1-2
Page Range:	S. 441 - 493
Date:	2014
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1823
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/42717