4,257 research outputs found
Upsilon invariants from cyclic branched covers
We extend the construction of upsilon-type invariants to null-homologous
knots in rational homology three-spheres. By considering -fold cyclic
branched covers with a prime power, this extension provides new knot
concordance invariants . We give computations of these
invariants for some families of alternating knots and reprove some independence
results.Comment: 26 pages, 13 figures. Comments are welcome
Towards a theory of local Shimura varieties
This is a survey article that advertizes the idea that there should exist a
theory of p-adic local analogues of Shimura varieties. Prime examples are the
towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also
review their theory in the light of this idea. We also discuss conjectures on
the -adic cohomology of local Shimura varieties.Comment: 53 page
Smashing localizations of rings of weak global dimension at most one
We show for a ring R of weak global dimension at most one that there is a
bijection between the smashing subcategories of its derived category and the
equivalence classes of homological epimorphisms starting in R. If, moreover, R
is commutative, we prove that the compactly generated localizing subcategories
correspond precisely to flat epimorphisms. We also classify smashing
localizations of the derived category of any valuation domain, and provide an
easy criterion for the Telescope Conjecture (TC) for any commutative ring of
weak global dimension at most one. As a consequence, we show that the TC holds
for any commutative von Neumann regular ring R, and it holds precisely for
those Pr\"ufer domains which are strongly discrete.Comment: 45 pages; version 2: several changes in the presentation (a section
on the homotopy category of dg algebras became an appendix, more explanation
added at various places of the text), main results unchange
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