170 research outputs found
Homotopy Ends and Thomason Model Categories
In the last year of his life, Bob Thomason reworked the notion of a model
category, used to adapt homotopy theory to algebra, and used homotopy ends to
affirmatively solve a problem raised by Grothendieck: find a notion of model
structure which is inherited by functor categories. In this paper we explain
and prove Thomason's results, based on his private notebooks.
The first half presents Thomason's ideas about homotopy ends and its
generalizations. This material may be of independent interest. Then we define
Thomason model categories and give some examples. The usual proof shows that
the homotopy category exists.
In the last two sections we prove the main theorem: functor categories
inherit a Thomason model structure, at least when the original category is
enriched over simplicial sets and fibrations are preserved by limits.Comment: 39 pages, AMS-TeX file using picte
Some surfaces of general type for which Bloch's conjecture holds
We give many examples of surfaces of general type with for which
Bloch's conjecture holds, for all values of except 9. Our surfaces are
equipped with an involution
Cotensor products of modules
Let C be a coalgebra over a field k and A its dual algebra. The category of
C-comodules is equivalent to a category of A-modules. We use this to interpret
the cotensor product M \square N of two comodules in terms of the appropriate
Hochschild cohomology of the A-bimodule M \otimes N, when A is
finite-dimensional, profinite, graded or differential-graded. The main
applications are to Galois cohomology, comodules over the Steenrod algebra, and
the homology of induced fibrations.Comment: 16 pages, LaTe
Relative Cartier divisors and K-theory
We study the relative Picard group of a map of schemes.
If is faithful affine, it is the relative Cartier divisor group . The
relative group has a -filtration, and is the top
quotient for the -filtration. When is induced by a ring
homomorphism , we show that the relative "nil" groups and
are continuous -modules
Slices of Co-Operations for
We verify a conjecture of Voevodsky, concerning the slices of co-operations
in motivic -theory.Comment: 20 page
Twisted K-theory, Real -bundles and Grothendieck-Witt groups
We introduce a general framework to unify several variants of twisted
topological -theory. We focus on the role of finite dimensional real simple
algebras with a product-preserving involution, showing that Grothendieck-Witt
groups provide interesting examples of twisted -theory. These groups are
linked with the classification of algebraic vector bundles on real algebraic
varieties
Unstable operations in \'etale and motivic cohomology
We classify all \'etale cohomology operations on H_\et^n(-,\muell{i}),
showing that they were all constructed by Epstein. We also construct operations
on the mod- motivic cohomology groups , differing from
Voevodsky's operations; we use them to classify all motivic cohomology
operations on and and suggest a general classification.Comment: 26 page
Principal ideals in mod- Milnor -theory
Fix a symbol in the mod- Milnor -theory of a field
, and a norm variety for . We show that the ideal
generated by is the kernel of the -theory map induced by
and give generators for the annihilator of the ideal. When
, this was done by Orlov, Vishik and Voevodsky.Comment: 14 page
K-theory of line bundles and smooth varieties
We give a -theoretic criterion for a quasi-projective variety to be
smooth. If is a line bundle corresponding to an ample invertible
sheaf on , it suffices that for all
.Comment: 11 page
Norm Varieties and the Chain Lemma (after Markus Rost)
The goal of this paper is to present proofs of two results of Markus Rost:
the Chain Lemma and the Norm Principle. These are the final steps needed to
complete the publishable verification of the Bloch-Kato conjecture, that the
norm residue maps are isomorphisms between Milnor K-theory and
etale cohomology for every prime p, every n and every field k
containing 1/p.
Our proofs of these two results are based on Rost's 1998 preprints, his web
site and Rost's lectures at the Institute for Advanced Study in 1999-2000 and
2005
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