Titlebook: Women in Numbers Europe II; Contributions to Num Irene I. Bouw,Ekin Ozman,Rachel Newton Conference proceedings 2018 The Author(s) and the A

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2364-5733 researchers in number theory.Provides an easily accessible iInspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the confere

Sciatica

Non-ordinary Curves with a Prym Variety of Low ,-Rank,uble cover . : . → . for which .. has .-rank 0 (and is thus supersingular); for 3 ≤ . ≤ 19, we verify the same for each 0 ≤ . ≤ 3. Using theoretical results about .-rank stratifications of moduli spaces, we prove, for small . and arbitrary . ≥ 3, that there exists an unramified double cover . : . → . such that both . and .. have small .-rank.

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Elliptic Fibrations on Covers of the Elliptic Modular Surface of Level 5,or which the double cover is branched over the two reducible fibers of type .. and for which it is branched over two smooth fibers, giving a complete list of elliptic fibrations for these two scenarios.

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创作

The a-Number of Hyperelliptic Curves,his paper, we show that this bound can be lowered to . < .. The method of proof is to force the Cartier-Manin matrix to have rank 1 and examine what restriction that places on the affine equation defining the hyperelliptic curve. We then use this bound to summarize what is known about the existence of such curves when . = 3, 5 and 7.

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Mundane

Reductions of Algebraic Integers II,ng the following condition: the reduction of . modulo . is well-defined and has size coprime to .. We show that the natural density of this set is a computable rational number by reducing to the case where . is prime, case which has been treated in the previous work . (joint with Christophe Debry, J

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秘方药

The a-Number of Hyperelliptic Curves,, over which the curve is defined. It was proven by Elkin that for a genus . hyperelliptic curve . to have .. = . − 1, the genus is bounded by .. In this paper, we show that this bound can be lowered to . < .. The method of proof is to force the Cartier-Manin matrix to have rank 1 and examine what r