On the nonexistence of certain curves of genus two

We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our proof uses the Brauer relations in a biquadratic extension of Q to show that every principally polarized abelian surface over F_q with the given characteristic polynomial splits over F_{q^2} as a product of polarized elliptic curves.Comment: LaTeX, 13 page

The Constitution and Capital Sentencing: Pursuing Justice and Equality

Equal Justice and The Death Penalty: A Legal and Empirical Analysis. By David C. Baldus, George Woodworth and Charles Pulaski, Jr. Boston: Northeastern University Press. 1990. Pp. Vii, 689. $65.0

Isogeny classes of abelian varieties with no principal polarizations

We provide a simple method of constructing isogeny classes of abelian varieties over certain fields k such that no variety in the isogeny class has a principal polarization. In particular, given a field k, a Galois extension l of k of odd prime degree p, and an elliptic curve E over k that has no complex multiplication over k and that has no k-defined p-isogenies to another elliptic curve, we construct a simple (p-1)-dimensional abelian variety X over k such that every polarization of every abelian variety isogenous to X has degree divisible by p^2. We note that for every odd prime p and every number field k, there exist l and E as above. We also provide a general framework for determining which finite group schemes occur as kernels of polarizations of abelian varieties in a given isogeny class. Our construction was inspired by a similar construction of Silverberg and Zarhin; their construction requires that the base field k have positive characteristic and that there be a Galois extension of k with a certain non-abelian Galois group.Comment: 13 pages, AMS-TeX, with updated references. To appear in the volume "Moduli of Abelian Varieties (Texel Island 1999)

The Efficient Water Market of the Northern Colorado Water Conservancy District: Colorado, USA

The case study presented is focused on the use of tradable and rentable water permits designed to maximise the efficiency of the use of water resources in Colorado (USA). The State of Colorado is divided into two distinct regions: the eastern, dry plains and the western areas that start with the Rocky Mountains and extend through rugged lands to the western border of the State. Rainfall and snow are heavy on the western side of the Rockies, while the eastern slopes of the mountains (the "East Slope") and the plains are semi-arid. In order to compensate this unequal distribution of the water resources, a complicated project of water transfer has been designed. The Colorado-Big Thompson Project is the largest transmountain water diversion project in Colorado. Built between 1938 and 1957, the C-BT Project provides supplemental water to 30 cities and towns and is used to provide supplemental irrigation to 693,000 acres of north-eastern. In order to efficiently manage the "foreign water provision" ensured by the CB-t project, it was founded the Northern Colorado Water Conservation District (NCWCD). It was established in 1937 to contract with the Federal Government to build the large trans-mountain water transfer project. NCWCD is responsible for the diversion works of the project and for the allocation of water on the eastern side of the mountains