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Defining Valuation Rings and Other Definability Problems in Number Theory

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No logo availableInstitut des Hautes Études Scientifiques (IHÉS)
 Shlapenkoth, Alexandra

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Defining Valuation Rings and Other Definability Problems in Number Theory
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10
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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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We discuss questions concerning first-order and existential definability over number fields and function fields in the language of rings and its extensions. In particular, we consider the problem of defining valuations rings over finite and infinite algebraic extensions of Q, and over function fields of arbitrary characteristic.