Hilbert schemeIn algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
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.
Formal schemeIn mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes.
Millennium Development GoalsThe Millennium Development Goals (MDGs) were eight international development goals for the year 2015 that had been established following the Millennium Summit of the United Nations in 2000, following the adoption of the United Nations Millennium Declaration. These were based on the OECD DAC International Development Goals agreed by Development Ministers in the "Shaping the 21st Century Strategy". The Sustainable Development Goals (SDGs) succeeded the MDGs in 2016.
Hedge fundA hedge fund is a pooled investment fund that trades in relatively liquid assets and is able to make extensive use of more complex trading, portfolio-construction, and risk management techniques in an attempt to improve performance, such as short selling, leverage, and derivatives. Financial regulators generally restrict hedge fund marketing to institutional investors, high net worth individuals, and accredited investors. Hedge funds are considered alternative investments.
Money creationMoney creation, or money issuance, is the process by which the money supply of a country, or of an economic or monetary region, is increased. In most modern economies, money creation is controlled by the central banks. Money issued by central banks is termed base money. Central banks can increase the quantity of base money directly, by engaging in open market operations. However, the majority of the money supply is created by the commercial banking system in the form of bank deposits.
Debt reliefDebt relief or debt cancellation is the partial or total forgiveness of debt, or the slowing or stopping of debt growth, owed by individuals, corporations, or nations. From antiquity through the 19th century, it refers to domestic debts, in particular agricultural debts and freeing of debt slaves. In World War I the United States Treasury made large loans to the allies that were postponed, reduced and finally paid off in 1953. In the late 20th century, it came to refer primarily to Third World debt, which started exploding with the Latin American debt crisis (Mexico 1983, etc.
Money supplyIn macroeconomics, the money supply (or money stock) refers to the total volume of currency held by the public at a particular point in time. There are several ways to define "money", but standard measures usually include currency in circulation (i.e. physical cash) and demand deposits (depositors' easily accessed assets on the books of financial institutions). The central bank of a country may use a definition of what constitutes legal tender for its purposes.
Fiber product of schemesIn mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special cases. For example, the fiber product describes how an algebraic variety over one field determines a variety over a bigger field, or the pullback of a family of varieties, or a fiber of a family of varieties. Base change is a closely related notion. The of schemes is a broad setting for algebraic geometry.
Sustainable Development GoalsThe Sustainable Development Goals or Global Goals are a collection of seventeen interlinked objectives designed to serve as a "shared blueprint for peace and prosperity for people and the planet, now and into the future." The SDGs are no poverty; zero hunger; good health and well-being; quality education; gender equality; clean water and sanitation; affordable and clean energy; decent work and economic growth; industry, innovation and infrastructure; reduced inequalities; sustainable cities and communities; responsible consumption and production; climate action; life below water; life on land; peace, justice, and strong institutions; and partnerships for the goals.
Demand for moneyIn monetary economics, the demand for money is the desired holding of financial assets in the form of money: that is, cash or bank deposits rather than investments. It can refer to the demand for money narrowly defined as M1 (directly spendable holdings), or for money in the broader sense of M2 or M3. Money in the sense of M1 is dominated as a store of value (even a temporary one) by interest-bearing assets. However, M1 is necessary to carry out transactions; in other words, it provides liquidity.
Velocity of moneyThe velocity of money measures the number of times that the average unit of currency is used to purchase goods and services within a given time period. The concept relates the size of economic activity to a given money supply, and the speed of money exchange is one of the variables that determine inflation. The measure of the velocity of money is usually the ratio of the gross national product (GNP) to a country's money supply. If the velocity of money is increasing, then transactions are occurring between individuals more frequently.
