6,375 research outputs found

    Topological modular forms with level structure

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    The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them. Along the way, we produce a natural way to restrict to the cusps, providing multiplicative maps from Tmf with level structure to forms of K-theory. In particular, this allows us to construct a connective spectrum tmf_0(3) consistent with properties suggested by Mahowald and Rezk. This is accomplished using the machinery of logarithmic structures. We construct a sheaf of locally even-periodic elliptic cohomology theories, equipped with highly structured multiplication, on the log-\'etale site of the moduli of elliptic curves. Evaluating this sheaf on modular curves produces Tmf with level structure.Comment: 53 pages. Heavily revised, including the addition of a new section on background tools from homotopy theor

    The spectra ko and ku are not Thom spectra: an approach using THH

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    We apply an announced result of Blumberg-Cohen-Schlichtkrull to reprove (under restricted hypotheses) a theorem of Mahowald: the connective real and complex K-theory spectra are not Thom spectra.Comment: 9 pages, 7 figure

    Climatic changes resulting from mass extinctions at the K-T boundary (and other bio-events)

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    The mass extinctions at the Cretaceous-Tertiary (K-T) boundary include about 90 percent of marine calcareous nannoplankton (coccoliths), and carbon-isotope data show that marine primary productivity was drastically reduced for about 500,000 years after the boundary event, the so-called Strangelove Ocean effect. One result of the elimination of most marine phytoplankton would have been a severe reduction in production of dimethyl sulfide (DMS), a biogenic gas that is believed to be the major precursor of cloud condensation nuclei (CCN) over the oceans. A drastic reduction in marine CCN should lead to a cloud canopy with significantly lower reflectivity, and hence cause a significant warming at the earth's surface. Calculations suggest that, all other things being held constant, a reduction in CCN of more than 80 percent (a reasonable value for the K-T extinctions) could have produced a rapid global warming of 6 C or more. Oxygen-isotope analyses of marine sediments, and other kinds of paleoclimatic data, have provided for a marked warming, and a general instability of climate coincident with the killoff of marine plankton at the K-T boundary. Similar reductions in phytoplankton abundance at other boundaries, as indicated by marked shifts in carbon-isotope curves, suggest that severe temperature changes may have accompanied other mass extinctions, and raises the intriguing possibility that the extinction events themselves could have contributed to the climatic instabilities at critical bio-events in the geologic record

    the Growth Potential for the Indiana Livestock Industries

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    Feed, processing capacity, population density versus animal density, and environmental capacities are the four different dimensions of livestock location and growth potential analyzed for Indiana. These four dimensions provide livestock producers, government officials, and livestock associations a valuable perspective on the constraints that could limit Indiana’s livestock growth potential. Comparisons among 21 states on these dimensions indicated that Indiana is a second choice of states for livestock growth; Kansas and Iowa are the only first choices. Indiana’s strength in the state comparison is its ability to assimilate the phosphorus produced by livestock and commercial phosphorus. As environmental regulations continue to tighten and shift from nitrogen to phosphorus based application standards for manure, the ability to assimilate phosphorus will continue to be one of Indiana’s strengths, along with its abundance of feed and swine processing capacity. Population density is the key dimension that is a disadvantage for Indiana. Within the state of Indiana, the West Central district has key advantages compared to other districts of the state. This district has an abundance of feed, the second lowest population density in the state, and excess phosphorus assimilation capacity. This district does not have processing capacity for any species, but the adjoining districts do have adequate processing capacity. Overall, the results show that Indiana has the potential to grow the livestock sector. However, there will be constraints such as population density that require more in-depth study to determine how to address this potential limitation on growth.Livestock Growth, Animal Waste, Feed Capacity, Livestock Processing Capacity, Animal Density, Population Density
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