Žetale

Žetale is a village and a municipality in eastern Slovenia, on the border with Croatia. The area traditionally belonged to the region of Styria. It is now included in the Drava statistical region.

History

The village of Čermožiše has evidence of a settlement from the neolithic era. Žetale was first mentioned in written documents dating to 1228, and old parish documents record its name as Schiltarin. The area was subject to repeated Ottoman invasion, and thus pseudoetymological claims that the village is named after a supposed defender of the village named Žetal. In fact, the name is derived from Middle High German Schiltern. As of 2002, the village of Žetale had a population of 390.

Festivals

A chestnut festival in October is a locally well known. There is an annual pilgrimage called Jarmek held on 15 August, the feast day of the Assumption of Mary and a public holiday in Slovenia, where pilgrims walk to the church of Mary Help of Christians (Slovene: Marija pomočnica), known locally as Marijatrošt.

Étale morphism

In algebraic geometry, an étale morphism (French: [eˈtal]) is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms. Despite this, étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology.

The word étale is a French adjective, which means "slack", as in "slack tide", or, figuratively, calm, immobile, something left to settle.

Definition

Let be a ring homomorphism. This makes an -algebra. Choose a monic polynomial in and a polynomial in such that the derivative of is a unit in . We say that is standard étale if and can be chosen so that is isomorphic as an -algebra to and is the canonical map.

Étale (mountain)

Étale is a mountain of Savoie and Haute-Savoie, France. It lies in the Aravis Range of the French Prealps and has an elevation of 2,484 metres above sea level.

References