Motives of Log Schemes
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Date
2017-09-06
Authors
Howell, Nicholas
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
This thesis introduces two notions of motive associated to a log
scheme. We introduce a category of log motives à la Voevodsky,
and prove that the embedding of Voevodsky motives is an equivalence, in
particular proving that any homotopy-invariant cohomology theory of
schemes extends uniquely to log schemes. In the case of a log smooth
degeneration, we give an explicit construction of the motivic Albanese
of the degeneration, and show that the Hodge realization of this
construction gives the Albanese of the limit Hodge structure.
Description
Keywords
Albanese, degeneration, limit Hodge structure, log geometry, motive