27,103 research outputs found
Comparing Euler classes
We establish the equality of two definitions of an Euler class in algebraic
geometry: the first definition is as a "characteristic class" with values in
Chow-Witt theory, while the second definition is as an "obstruction class."
Along the way, we refine Morel's relative Hurewicz theorem in A^1-homotopy
theory, and show how to define (twisted) Chow-Witt groups for geometric
classifying spaces.Comment: 33 pages; Final version (before proofs). To appear Q. J. Mat
Lattice-ordered abelian groups and perfect MV-algebras: a topos-theoretic perspective
We establish, generalizing Di Nola and Lettieri's categorical equivalence, a
Morita-equivalence between the theory of lattice-ordered abelian groups and
that of perfect MV-algebras. Further, after observing that the two theories are
not bi-interpretable in the classical sense, we identify, by considering
appropriate topos-theoretic invariants on their common classifying topos, three
levels of bi-intepretability holding for particular classes of formulas:
irreducible formulas, geometric sentences and imaginaries. Lastly, by
investigating the classifying topos of the theory of perfect MV-algebras, we
obtain various results on its syntax and semantics also in relation to the
cartesian theory of the variety generated by Chang's MV-algebra, including a
concrete representation for the finitely presentable models of the latter
theory as finite products of finitely presentable perfect MV-algebras. Among
the results established on the way, we mention a Morita-equivalence between the
theory of lattice-ordered abelian groups and that of cancellative
lattice-ordered abelian monoids with bottom element.Comment: 54 page
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