3,658 research outputs found

    Rational S^1-equivariant elliptic cohomology

    Get PDF
    For each elliptic curve A over the rational numbers we construct a 2-periodic S^1-equivariant cohomology theory E whose cohomology ring is the sheaf cohomology of A; the homology of the sphere of the representation z^n is the cohomology of the divisor A(n) of points with order dividing n. The construction proceeds by using the algebraic models of the author's AMS Memoir ``Rational S^1 equivariant homotopy theory.'' and is natural and explicit in terms of sheaves of functions on A. This is Version 5.2 of a paper of long genesis (this should be the final version). The following additional topics were first added in the Fourth Edition: (a) periodicity and differentials treated (b) dependence on coordinate (c) relationship with Grojnowksi's construction and, most importantly, (d) equivalence between a derived category of O_A-modules and a derived category of EA-modules. The Fifth Edition included (e) the Hasse square and (f) explanation of how to calculate maps of EA-module spectra

    Crystallographic groups and flat manifolds from complex reflection groups

    Full text link
    Following an idea of Gon\c{c}alvez, Guaschi and Ocampo on the usual braid group we construct crystallographic and Bieberbach groups as (sub)quotients of the generalized braid group associated to an arbitrary complex reflection group.Comment: 13 pages. V2 : minor improvement

    On the K-theory of truncated polynomial algebras over the integers

    Full text link
    We show that the K_{2i}(Z[x]/(x^m),(x)) is finite of order (mi)!(i!)^{m-2} and that K_{2i+1}(Z[x]/(x^m),(x)) is free abelian of rank m-1. This is accomplished by showing that the equivariant homotopy groups of the topological Hochschild spectrum THH(Z) are finite, in odd degrees, and free abelian, in even degrees, and by evaluating their orders and ranks, respectively.Comment: Journal of Topology (to appear

    Semistable abelian varieties and maximal torsion 1-crystalline submodules

    Get PDF
    Let pp be a prime, let KK be a discretely valued extension of Qp\mathbb{Q}_p, and let AKA_{K} be an abelian KK-variety with semistable reduction. Extending work by Kim and Marshall from the case where p>2p>2 and K/QpK/\mathbb{Q}_p is unramified, we prove an l=pl=p complement of a Galois cohomological formula of Grothendieck for the ll-primary part of the N\'eron component group of AKA_{K}. Our proof involves constructing, for each m∈Z≥0m\in \mathbb{Z}_{\geq 0}, a finite flat OK\mathscr{O}_K-group scheme with generic fiber equal to the maximal 1-crystalline submodule of AK[pm]A_{K}[p^{m}]. As a corollary, we have a new proof of the Coleman-Iovita monodromy criterion for good reduction of abelian KK-varieties.Comment: Fixed typos and added funding acknowledgemen
    • …
    corecore