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Characterizing algebraic stacks
Author(s):
Sharon
Hollander
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1465-1476.
MSC (2000):
Primary 55U10;
Secondary 18G55, 14A20
Posted:
December 6, 2007
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Abstract:
We extend the notion of algebraic stack to an arbitrary subcanonical site  . If the topology on  is local on the target and satisfies descent for morphisms, we show that algebraic stacks are precisely those which are weakly equivalent to representable presheaves of groupoids whose domain map is a cover. This leads naturally to a definition of algebraic  -stacks. We also compare different sites naturally associated to a stack.
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Additional Information:
Sharon
Hollander
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel
Address at time of publication:
Centro de Análise Mathematica, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Tech. Univ. Lisbon, Portugal
Email:
sjh@math.ist.utl.pt
DOI:
10.1090/S0002-9939-07-08832-6
PII:
S 0002-9939(07)08832-6
Received by editor(s):
May 30, 2006
Received by editor(s) in revised form:
June 29, 2006
Posted:
December 6, 2007
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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