The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite dimensional ; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent ; this reduces to Serre's theorem over a one-point space.

The map shows both the Angeln and the Schwansen peninsulas

The base does not appear on public U. S. government maps ; the USGS topographic map for the area only shows the long-disused Groom Mine.

A map of Cyprus in the later Bronze Age ( such as is given by J. L. Myres and M. O. Richter in Catalogue of the Cyprus Museum ) shows more than 25 settlements in and about the Mesaorea district alone, of which one, that at Enkomi, near the site of Salamis, has yielded the richest Aegean treasure in precious metal found outside Mycenae.

The latest Ordnance Survey Ireland " Discovery Series " ( Third Edition 2005 ) 1: 50, 000 map of the Dublin Region, Sheet 50, shows the boundaries of the city and three surrounding counties of the region.

Information richness or a map that is multivariate shows relationships within the map.

This issue assumes more importance as the scale of the map gets smaller ( i. e. the map shows a larger area ) because the information shown on the map takes up more space on the ground.

This map of the world in 1914 shows the large colonial empires that powerful nations established across the globe

* ESP shows textual information about the enemy ; such as health, name and distance ; also information about weapons lying around the map, which could be missed without the hack.

The Sebastian Cabot map ( Antwerp 1544 ) shows a number of islands to the south which may be the Mascarene Islands.

This electrostatic potential map shows how the oxygen atom has a more negative charge ( red ) than the positive ( blue ) hydrogen atoms of a water molecule.

The map also shows Hong Kong's maritime boundaries.

The map at the beginning of this article shows the 32 traditional counties that were in place in Ireland by early 17th century.

A 1905 map shows the Khazar empire in 814.

This 1856 map shows slave states ( gray ), free states ( pink ), U. S. territories ( green ), and Kansas in center ( white ).

A map of the world in the years 1920 – 1945, which shows the League of Nations members during its history

As the map shows, the firestorm jumped natural firebreaks ( river channels ), as well as prepared firebreaks.

* Macbeth's Scotland on Google Maps This map shows some of the primary locations in Macbeth.

This map shows the boundary of 13th century Mongol Empire and location of today's Mongols in modern Mongolia, Russia, Central Asia n States and People's Republic of China | China.

The national Railroad Development Corporation map shows a proposed extension across the border to Chipata in Zambia.

The map also shows the 75th parallel north and 60th parallel north.

Now let us imagine a wing of B-52's, on alert near their `` positive control ( or fail-safe ) points '', the spots on the map, many miles from Soviet territory, beyond which they are forbidden to fly without specific orders to proceed to their targets.

Public-spirited backers staked him to a brand-new airplane, aimed at putting their city and state on the flying map.

The Samaritans of Samaria ( see map at Iudaea Province ), had their temple on Mount Gerizim, and along with some other differences, see Samaritanism, were in conflict with Jews of Judea and Galilee and other regions who had their Temple in Jerusalem and practiced Judaism.

Some scientists believe it has to do with a kind of neural map that the brain has of the body, which sends information to the rest of the brain about limbs regardless of their existence.

This is the most natural configuration for memory, as all combinations of their address lines map to a valid address, allowing easy aggregation into a larger block of memory with contiguous addresses.

The game between the Chicago Cubs and St. Louis Cardinals in particular was cited for putting Ryne Sandberg ( as well as the 1984 Cubs in general, who would go on to make their first postseason appearance since 1945 ) " on the map.

The choice does affect their starting position on the " Play on Earth " map, and thus different resources in one's initial cities, but has no effect on starting position when starting a random world game or a customized world game.

A map showing the Great Lakes and their Drainage basin | watershed, with State, Provincial and International boundaries.

Those countries marked in dark blue on the map above use Western European Summer Time and advance their clock one hour in summer.

Cartographers must decide and then adjust the content within their maps to create a suitable and useful map that conveys geospatial information within their representation of the world.

This put both Belle & Sebastian and Jeepster firmly on the map, and enabled them to release several EPs with Belle & Sebastian throughout 1997, as well as signing their second act, Snow Patrol, later in the year.

Professional diplomats like Weizsäcker who had never accepted the legitimacy of Poland, which they saw as an " abomination " created by the Versailles treaty, were whole-hearted in their support of a war to wipe Poland off the map.

they are used only as intermediate constructs in map projections of the reference ellipsoid to the plane: their numerical values are not of interest.

Software packages can extend the concept of mind mapping by allowing individuals to map more than thoughts and ideas with information on their computers and the internet, like spreadsheets, documents, internet sites and images.

* Azimuthal or Gnomonic map projections are often used in planning air routes due to their ability to represent great circles as straight lines.

An active research topic in marine biology is to discover and map the life cycles of various species and where they spend their time.

Captain John Smith of Jamestown | John Smith's 1624 map of the Somers Isles ( Bermuda ), showing St. George's, Bermuda | St. George's Town and related fortifications, including the Castle Islands Fortifications, Bermuda | Castle Islands Fortifications with their garrisons of militiamen

On their 1614 map, which gave them a four year trade monopoly under a patent of the States General, they named the newly discovered and mapped territory New Netherland for the first time.

The Picts were probably tributary to Northumbria until the reign of Bridei map Beli, when the Anglians suffered a defeat at the Battle of Dun Nechtain that halted their northward expansion.

If a player dies all their weapons are lost and they receive the spawn weapons for the current map, usually the gauntlet and machine gun.

From its earliest stirrings, with their focus on the development of national languages and folklore, and the spiritual value of local customs and traditions, to the movements that would redraw the map of Europe and lead to calls for " self-determination " of nationalities, nationalism was one of the key issues in Romanticism, determining its roles, expressions and meanings.