1,809 research outputs found
T-motives
Considering a (co)homology theory on a base category
as a fragment of a first-order logical theory we here construct
an abelian category which is universal with respect
to models of in abelian categories. Under mild conditions on the
base category , e.g. for the category of algebraic schemes, we get
a functor from to
the category of chain complexes of ind-objects of .
This functor lifts Nori's motivic functor for algebraic schemes defined over a
subfield of the complex numbers. Furthermore, we construct a triangulated
functor from to Voevodsky's motivic
complexes.Comment: Added reference to arXiv:1604.00153 [math.AG
Predicative toposes
We explain the motivation for looking for a predicative analogue of the
notion of a topos and propose two definitions. For both notions of a
predicative topos we will present the basic results, providing the groundwork
for future work in this area
Etale homotopy types of moduli stacks of algebraic curves with symmetries
Using the machinery of etale homotopy theory a' la Artin-Mazur we determine
the etale homotopy types of moduli stacks over \bar{\Q} parametrizing
families of algebraic curves of genus g greater than 1 endowed with an action
of a finite group G of automorphisms, which comes with a fixed embedding in the
mapping class group, such that in the associated complex analytic situation the
action of G is precisely the differentiable action induced by this specified
embedding of G in the mapping class group.Comment: 27 page
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