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- W4255153620 abstract "This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadratic extension, a tamely ramified division algebra, a ramified separable quadratic extension, and a unique unramified quaternion division algebra. The chapter also describes ramified quaternion division algebras <italic>D</italic>₁, <italic>D</italic>₂, and <italic>D</italic>₃ over <italic>K</italic> containing a common subfield <italic>E</italic> such that <italic>E</italic>/<italic>K</italic> is a ramified separable extension." @default.
- W4255153620 created "2022-05-12" @default.
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- W4255153620 date "2017-10-19" @default.
- W4255153620 modified "2023-09-25" @default.
- W4255153620 title "Existence" @default.
- W4255153620 doi "https://doi.org/10.23943/princeton/9780691166902.003.0016" @default.
- W4255153620 hasPublicationYear "2017" @default.
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