Descent via (5,5)-isogeny on Jacobians of genus 2 curves

AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J is the Jacobian variety of C, and develop the theory required to perform descent via (5,5)-isogeny. We apply this to several examples, where it can be shown that non-reducible Jacobians have nontrivial 5-part of the Tate–Shafarevich group

Large rational torsion on abelian varieties

A method of searching for large rational torsion on Abelian varieties is described. A few explicit applications of this method over Q give rational 11- and 13-torsion in dimension 2, and rational 29-torsion in dimension 4

Extending Elliptic Curve Chabauty to higher genus curves

We give a generalization of the method of "Elliptic Curve Chabauty" to higher genus curves and their Jacobians. This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell-Weil sieve to provide a complete solution to the problem of determining the set of rational points of an algebraic curve $Y$.Comment: 24 page

Galois sections for abelianized fundamental groups

Given a smooth projective curve $X$ of genus at least 2 over a number field $k$, Grothendieck's Section Conjecture predicts that the canonical projection from the \'etale fundamental group of $X$ onto the absolute Galois group of $k$ has a section if and only if the curve has a rational point. We show that there exist curves where the above map has a section over each completion of $k$ but not over $k$. In the appendix Victor Flynn gives explicit examples in genus 2. Our result is a consequence of a more general investigation of the existence of sections for the projection of the \'etale fundamental group `with abelianized geometric part' onto the Galois group. We give a criterion for the existence of sections in arbitrary dimension and over arbitrary perfect fields, and then study the case of curves over local and global fields more closely. We also point out the relation to the elementary obstruction of Colliot-Th\'el\`ene and Sansuc.Comment: This is the published version, except for a characteristic 0 assumption added in Section 5 which was unfortunately omitted there. Thanks to O. Wittenberg for noticing i

Materiality, health informatics and the limits of knowledge production

© IFIP International Federation for Information Processing 2014 Contemporary societies increasingly rely on complex and sophisticated information systems for a wide variety of tasks and, ultimately, knowledge about the world in which we live. Those systems are central to the kinds of problems our systems and sub-systems face such as health and medical diagnosis, treatment and care. While health information systems represent a continuously expanding field of knowledge production, we suggest that they carry forward significant limitations, particularly in their claims to represent human beings as living creatures and in their capacity to critically reflect on the social, cultural and political origins of many forms of data ‘representation’. In this paper we take these ideas and explore them in relation to the way we see healthcare information systems currently functioning. We offer some examples from our own experience in healthcare settings to illustrate how unexamined ideas about individuals, groups and social categories of people continue to influence health information systems and practices as well as their resulting knowledge production. We suggest some ideas for better understanding how and why this still happens and look to a future where the reflexivity of healthcare administration, the healthcare professions and the information sciences might better engage with these issues. There is no denying the role of health informatics in contemporary healthcare systems but their capacity to represent people in those datascapes has a long way to go if the categories they use to describe and analyse human beings are to produce meaningful knowledge about the social world and not simply to replicate past ideologies of those same categories