3,658 research outputs found
Rational S^1-equivariant elliptic cohomology
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
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
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
Let be a prime, let be a discretely valued extension of
, and let be an abelian -variety with semistable
reduction. Extending work by Kim and Marshall from the case where and
is unramified, we prove an complement of a Galois
cohomological formula of Grothendieck for the -primary part of the N\'eron
component group of . Our proof involves constructing, for each , a finite flat -group scheme with generic
fiber equal to the maximal 1-crystalline submodule of . As a
corollary, we have a new proof of the Coleman-Iovita monodromy criterion for
good reduction of abelian -varieties.Comment: Fixed typos and added funding acknowledgemen
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