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000938662 019__ $$a1175919047$$a1178998173$$a1182449815$$a1182914441$$a1183926719
000938662 020__ $$a9783030437817$$q(electronic book)
000938662 020__ $$a3030437817$$q(electronic book)
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000938662 0247_ $$a10.1007/978-3-030-43
000938662 035__ $$aSP(OCoLC)on1179050260
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000938662 1001_ $$aCoray, D. F.$$q(Daniel F.)
000938662 24510 $$aNotes on geometry and arithmetic /$$cDaniel Coray.
000938662 260__ $$aCham :$$bSpringer,$$c2020.
000938662 300__ $$a1 online resource
000938662 336__ $$atext$$btxt$$2rdacontent
000938662 337__ $$acomputer$$bc$$2rdamedia
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000938662 4901_ $$aUniversitext
000938662 504__ $$aIncludes bibliographical references and index.
000938662 506__ $$aAccess limited to authorized users.
000938662 520__ $$aThis English translation of Daniel Corays original French textbook Notes de géométrie et darithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the most essential ideas from algebraic geometry and commutative algebra. Readers are invited to discover rational points on varieties through an appealing 'hands on approach that offers a pathway toward active research in arithmetic geometry. Along the way, the reader encounters the state of the art on solving certain classes of polynomial equations with beautiful geometric realizations, and travels a unique ascent towards variations on the Hasse Principle. Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilberts Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.
000938662 650_0 $$aArithmetical algebraic geometry.
000938662 650_0 $$aGeometry.
000938662 77608 $$iPrint version: $$z3030437809$$z9783030437800$$w(OCoLC)1141931110
000938662 830_0 $$aUniversitext.
000938662 852__ $$bebk
000938662 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-43781-7$$zOnline Access$$91397441.1
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000938662 980__ $$aBIB
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