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Algebraic geometry over the residue field of the infinite place

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  • Márton Hablicsek
  • Máté L. Juhász

Nikolai Durov introduced the theory of generalized rings and schemes to study Arakelov geometry in an alternative algebraic framework, and introduced the residue field at the infinite place, 픽. We show an elementary algebraic approach to modules and algebras over this object, define prime congruences, show that the polynomial ring of n variables is of Krull dimension n, and derive a prime decomposition theorem for these primes.

OriginalsprogEngelsk
TidsskriftCommunications in Algebra
Vol/bind46
Udgave nummer10
Sider (fra-til)4149-4173
Antal sider25
ISSN0092-7872
DOI
StatusUdgivet - 2018
Eksternt udgivetJa

ID: 215778300