Triple Massey products vanish over all fields

We show that the absolute Galois group of any field has the vanishing triple Massey product property. Several corollaries for the structure of maximal pro-$p$-quotient of absolute Galois groups are deduced. Furthermore, the vanishing of some higher Massey products is proved.Comment: We have improved our exposition following the referee's suggestions. The article will appear in the Journal of the London Mathematical Societ

Embedding problems with local conditions and the admissibility of finite groups

Let $k$ be a field of characteristic $p>0$, which has infinitely many discrete valuations. We show that every finite embedding problem for \Gal(k) with finitely many prescribed local conditions, whose kernel is a $p$-group, is properly solvable. We then apply this result in studying the admissibility of finite groups over global fields of positive characteristic. We also give another proof for a result of Sonn.Comment: 8 page

Economic impact of farmers-driven vertical integration: the case of safe vegetable chains in Northern Vietnam

The paper investigates the respective profitability of contractual arrangements, direct sales and spot marketing for "safe vegetable" farmers in Northern Vietnam. This is based on a survey of 137 peri-urban vegetable farmers, with a minimum of 30 farmers in each category. Selection biases are corrected using propensity score matching methods. The results show that direct sales have a positive significant impact on income relative to contractual arrangements and spot marketing when selection biases are corrected. Contractual arrangements have no significant impact on income compared with the other two categories after correction of selection bias. This may be due to the involvement of purchasers in the production process being still limited. The paper illustrates that direct relations between farmers and consumers, often described in the literature as efficient in the development of consumer confidence as regards quality, can indeed translate into higher incomes than anonymous exchange, or than contractual arrangements with retailing companies. Some limitations of the research and policy recommendations are given in the conclusion. (Résumé d'auteur

Triple Massey products over global fields

Let $K$ be a global field which contains a primitive $p$-th root of unity, where $p$ is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for $p=2$, any triple Massey product over $K$ with respect to $\mathbb{F}_p$, contains 0 whenever it is defined. We show that this is true for all primes $p$.Comment: The final version of this paper appeared in Documenta Mathematica, Vol. 20 (2015) 1467-148