[Q]: Question: "Under what theory is the relationship between the structure of groups and the structure of fields being studied?" Context: "for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the etale fundamental group." Answer:
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[A]: Galois

[Q]: Question: "What can be a reason for their traditions?" Context: "Much of the Alpine culture is unchanged since the medieval period when skills that guaranteed survival in the mountain valleys and in the highest villages became mainstays, leading to strong traditions of carpentry, woodcarving, baking and pastry-making, and cheesemaking." Answer:
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[A]: mountain valleys and in the highest villages became mainstays

[Q]: Question: "How often is Ann Arbor Art Fairs?" Context: "Several annual eventsmany of them centered on performing and visual artsdraw visitors to Ann Arbor. One such event is the Ann Arbor Art Fairs, a set of four concurrent juried fairs held on downtown streets. Scheduled on Wednesday through Saturday of the third week of July, the fairs draw upward of half a million visitors. Another is the Ann Arbor Film Festival, held during the third week of March, which receives more than 2,500 submissions annually from more than 40 countries and serves as one of a handful of Academy Awardqualifying festivals in the United States." Answer:
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[A]: annually

[Q]: Question: "What is a reason that the use of computers became more widely used?" Context: "In time, the network spread beyond academic and military institutions and became known as the Internet. The emergence of networking involved a redefinition of the nature and boundaries of the computer. Computer operating systems and applications were modified to include the ability to define and access the resources of other computers on the network, such as peripheral devices, stored information, and the like, as extensions of the resources of an individual computer. Initially these facilities were available primarily to people working in high-tech environments, but in the 1990s the spread of applications like e-mail and the World Wide Web, combined with the development of cheap, fast networking technologies like Ethernet and ADSL saw computer networking become almost ubiquitous. In fact, the number of computers that are networked is growing phenomenally. A very large proportion of personal computers regularly connect to the Internet to communicate and receive information. "Wireless" networking, often utilizing mobile phone networks, has meant networking is becoming increasingly ubiquitous even in mobile computing environments." Answer:
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[A]:
cheap, fast networking technologies