A Voevodsky motive associated to a log scheme
Georgii Shuklin

TL;DR
This paper constructs a new Voevodsky motive associated with fs log schemes over a field, linking it to log Betti cohomology and exploring applications in motivic neighborhoods and monodromy filtrations.
Contribution
It introduces a geometrical Voevodsky motive for fs log schemes and establishes its relation to log Betti cohomology over complex numbers.
Findings
Betti realization of the motive matches log Betti cohomology
Applications to motivic tubular neighborhoods
Insights into limit motives and monodromy filtrations
Abstract
For each fs log scheme over a field we construct a geometrical Voevodsky motive . We prove that, for , the Betti realization of is the log Betti cohomology of . We give applications to motivic tubular neighborhoods, limit motives and the monodromy filtrations.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Alkaloids: synthesis and pharmacology · Commutative Algebra and Its Applications
