arXiv subjects
Publications and source records attributed to Adam Morgan.
We will define new constructions similar to the graph systems of correspondences described by Deaconu et al. We will use these to prove a version of Ionescu's theorem for higher rank graphs. Afterwards we will examine the properties of these constructions further and make contact with Yeend's topological k-graphs and the tensor groupoid valued product systems of Fowler and Sims.
Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor product of the Cuntz-Pimsner algebra of X and the Cuntz=Pimsner algebra of Y. Furthermore, this subalgebra can be described in a natural way in terms of the gauge actions on the Cuntz-Pimsner algebras. We explore implications for graph algebras, crossed products by the integers, and crossed products by completely positive maps. We also give a new proof of a result of Kaliszewski and Quigg related to coactions on correspondences.
CfAIR2 is a large homogeneously reduced set of near-infrared (NIR) light curves for Type Ia supernovae (SN Ia) obtained with the 1.3m Peters Automated InfraRed Imaging TELescope (PAIRITEL). This data set includes 4607 measurements of 94 SN Ia and 4 additional SN Iax observed from 2005-2011 at the Fred Lawrence Whipple Observatory on Mount Hopkins, Arizona. CfAIR2 includes JHKs photometric measurements for 88 normal and 6 spectroscopically peculiar SN Ia in the nearby universe, with a median redshift of z~0.021 for the normal SN Ia. CfAIR2 data span the range from -13 days to +127 days from B-band maximum. More than half of the light curves begin before the time of maximum and the coverage typically contains ~13-18 epochs of observation, depending on the filter. We present extensive tests that verify the fidelity of the CfAIR2 data pipeline, including comparison to the excellent data of the Carnegie Supernova Project. CfAIR2 contributes to a firm local anchor for supernova cosmology studies in the NIR. Because SN Ia are more nearly standard candles in the NIR and are less vulnerable to the vexing problems of extinction by dust, CfAIR2 will help the supernova cosmology community develop more precise and accurate extragalactic distance probes to improve our knowledge of cosmological parameters, including dark energy and its potential time variation.
We study the 2-parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove the conjecture over quadratic extensions of the base field. The proof proceeds via a generalisation of a formula of Kramer and Tunnell relating local invariants of the curve, which may be of independent interest. A new feature of this generalisation is the appearance of terms which govern whether or not the Cassels--Tate pairing on the Jacobian is alternating, which first appeared in work of Poonen--Stoll. We establish the local formula in many instances and show that in remaining cases it follows from standard global conjectures.