Derived algebraic geometryDerived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over ), simplicial commutative rings or -ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g., Tor) of the structure sheaf. Grothendieck's scheme theory allows the structure sheaf to carry nilpotent elements.
Al-QaedaAl-Qaeda is a Sunni pan-Islamist militant organization led by Salafi jihadists who self-identify as a vanguard spearheading a global Islamist revolution to unite the Muslim world under a supra-national Islamic state known as the Caliphate. Its members are mostly composed of Arabs, but also include other peoples. Al-Qaeda has mounted attacks on civilian and military targets in various countries, including the 1998 United States embassy bombings and the September 11 attacks; it has been designated as a terrorist group by the United Nations Security Council, the North Atlantic Treaty Organization (NATO), the European Union, and various countries around the world.
Time zoneA time zone is an area which observes a uniform standard time for legal, commercial and social purposes. Time zones tend to follow the boundaries between countries and their subdivisions instead of strictly following longitude, because it is convenient for areas in frequent communication to keep the same time. All time zones are defined as offsets from Coordinated Universal Time (UTC), ranging from UTC−12:00 to UTC+14:00. The offsets are usually a whole number of hours, but a few zones are offset by an additional 30 or 45 minutes, such as in India, South Australia and Nepal.
Islamic StateThe Islamic State (IS), also known as the Islamic State of Iraq and the Levant (ISIL; ˈaɪsᵻl), Islamic State of Iraq and Syria (ISIS; ˈaɪsᵻs), and by its Arabic acronym Da'ish or Daesh (داعش, Dāʿish, ˈdaːʕɪʃ), is a transnational militant Islamist terrorist group and former unrecognized quasi-state that follows the Salafi jihadist branch of Sunni Islam. It was founded by Abu Musab al-Zarqawi in 1999 and gained global prominence in 2014, when it captured a large amount of Iraqi territory, and took advantage of the civil war in Syria to take control of chunks of territory in Eastern Syria.
Group schemeIn mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance.
