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We outline a method for the construction of hyperelliptic curves of genus 2 over small number fields whose Jacobian has complex multiplication and ordinary good reduction at the prime 3. We prove the existence of a quasi-quadratic time algorithm for canonically lifting in characteristic 3 based on equations defining a higher dimensional analogue of the… (More)

- Robert Carls
- 2009

In this article we compute equations satisfied by the canonical theta null point of the canonical lift of an ordinary abelian variety in characteristic 2. In contrast to the equations studied by J.-F. Mestre et al. ours are valid over an arbitrary 2-adic ring which possibly is of positive characteristic.

- Robert Carls, David Lubicz
- 2008

In this article we give an algorithm for the computation of the number of rational points on the Jacobian variety of a generic ordinary hyperelliptic curve defined over a finite field Fq of cardinality q with time complexity O(n) and space complexity O(n), where n = log(q). In the latter complexity estimate the genus and the characteristic are assumed as… (More)

- Robert Carls
- 2008

In this article we prove the existence of a canonical theta structure for the canonical lift of an ordinary abelian variety.

- Robert Carls, Ryan S. Hanson
- Journal of bacteriology
- 1971

A technique was developed for the detection, on agar, of mutants of Bacillus subtilis that lacked a functional tricarboxylic acid cycle. Mutants devoid of detectable levels of aconitase, isocitric dehydrogenase, alpha-ketoglutarate dehydrogenase, succinic dehydrogenase, fumarase, and malate dehydrogenase have been isolated and characterized. Several mutants… (More)

Then Ux is an open affine subvariety of X such that g(Ux) = Ux and ρg(x) ∈ Ux for all g ∈ G. We have X = ∪x∈XUx. The claim now follows from the quasicompactness of X with respect to the Zariski topology. By the above we can construct the quotient locally and obtain a global quotient by gluing affine pieces. Now assume that X is an affine variety. Let A =… (More)

Note that r is an order in R. We call r the order of (A, ι). We say that K is a field of definition for (A, ι) if K is a field of definition for A and all endomorphisms in ι(r) are defined over K. We remark that if K is a field of definition for A then there exists a finite extension L of K such that (A, ι) is defined over L. In the following let (A, ι) be… (More)

- Robert Carls
- 2008

In this article we prove the existence of a canonical theta structure for the canonical lift of an ordinary abelian variety.

- Robert Carls
- 2008

In this article we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain p-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application we give a purely algebraic proof of some 2-adic theta identities which… (More)

In this article we compute equations satisfied by the theta null point of a canonical lift in the case of residue field characteristic 2.