We construct del Pezzo surfaces of degree 4 violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of K3 surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.

Borrowing from a classical construction for counterexamples to the Hasse principle, we show that for a certain family of affine varieties which do not satisfy the Hasse principle, the Brauer-Manin obstruction is not satisfied. The approach is elementary and requires little algebraic geometry.

Let K be a complete discretely valued field of mixed characteristic (0, p) with possibly imperfect residue field. We prove a Hasse-Arf theorem for the arithmetic ramification filtrations [2] on GK , except possibly in the absolutely unramified and non-logarithmic case, or p = 2 and logarithmic case. As an application, we obtain a Hasse-Arf theorem for filtrations on finite flat group schemes ov...

A new version release (2.0) of the molecular simulation tool ms2 [S. Deublein, B. Eckl, J. Stoll, S. V. Lishchuk, G. Guevara-Carrion, C. W. Glass, T. Merker, M. Bernreuther, H. Hasse, J. Vrabec, Comput. Phys. Commun. 182 (2011) 2350] is presented. Version 2.0 features a hybrid parallelization based on MPI and OpenMP for molecular dynamics simulation to achieve higher scalability. Furthermore, t...

We present novel algorithms to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f(x) ∈ Fq[x] to be factored) with respect to a Drinfeld module φ with complex multiplication. Factors of f(x) supported on prime ideals with supersingular reducti...

et E be an elliptic curve defined over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we describe a reinterpretation of the Equivariant Tamagawa Number Conjecture (‘ETNC’) for E, F/k and p as an explicit family of p-adic congruences involving values of derivatives of the Hasse-Weil L-functions of twists of E, norma...

Let Q(k, l) be a poset whose Hasse diagram is a regular spider with k+1 legs having the same length l (cf. Fig. 1). We show that for any n ≥ 1 the nth cartesian power of the spider poset Q(k, l) is a Macaulay poset for any k ≥ 0 and l ≥ 1. In combination with our recent results [2] this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices,...