12,685 research outputs found
On simplicial commutative algebras with Noetherian homotopy
In this paper, a strategy is developed studying a simplicial commutative
algebra A whose zeroth homotopy group is a Noetherian ring B and whose higher
homotopy groups are finite over B. The strategy replaces A with a connected
simplicial supplemented k(q)-algebra, for each prime ideal q in B, which
preserves much of the Andre-Quillen homology of A. The methods for this
construction involves a mixture of methods of homotopy theory (e.g. Postnikov
towers) with methods of commutative algebras (e.g. completions, Cohen
factorizations). We finish by indicating how these methods resolve a more
general form of a conjecture posed by Quillen.Comment: 10 page
Simplicial commutative algebras with vanishing Andre-Quillen homology
In this paper, we study the Andr\'e-Quillen homology of simplicial
commutative -algebras, a field, having certain vanishing
properties. When has non-zero characteristic, we obtain an algebraic
version of a theorem of J.-P. Serre and Y. Umeda that characterizes such
simplicial algebras having bounded homotopy groups. We further discuss how this
theorem fails in the rational case and, as an application, indicate how the
algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for
algebras of finite type over Noetherian rings, which have non-zero
characteristic.Comment: 11 page
Weak convergence of the localized disturbance flow to the coalescing Brownian flow
We define a new state-space for the coalescing Brownian flow, also known as
the Brownian web, on the circle. The elements of this space are families of
order-preserving maps of the circle, depending continuously on two time
parameters and having a certain weak flow property. The space is equipped with
a complete separable metric. A larger state-space, allowing jumps in time, is
also introduced, and equipped with a Skorokhod-type metric, also complete and
separable. We prove that the coalescing Brownian flow is the weak limit in this
larger space of a family of flows which evolve by jumps, each jump arising from
a small localized disturbance of the circle. A local version of this result is
also obtained, in which the weak limit law is that of the coalescing Brownian
flow on the line. Our set-up is well adapted to time-reversal and our weak
limit result provides a new proof of time-reversibility of the coalescing
Brownian flow. We also identify a martingale associated with the coalescing
Brownian flow on the circle and use this to make a direct calculation of the
Laplace transform of the time to complete coalescence.Comment: Published at http://dx.doi.org/10.1214/13-AOP845 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org). arXiv admin note: substantial text
overlap with arXiv:0810.021
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