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- Arithmetic_surface abstract "In mathematics, an arithmetic surface over a Dedekind domain R with fraction field is a geometric object having one conventional dimension, and one other dimension provided by the infinitude of the primes. When R is the ring of integers Z, this intuition depends on the prime ideal spectrum Spec(Z) being seen as analogous to a line. Arithmetic surfaces arise naturally in diophantine geometry, when an algebraic curve defined over K is thought of as having reductions over the fields R/P, where P is a prime ideal of R, for almost all P; and are helpful in specifying what should happen about the process of reducing to R/P when the most naive way fails to make sense.Such an object can be less informally defined as an R-scheme with a non-singular, connected projective curve for a generic fiber and unions of curves (possibly reducible, singular, non-reduced ) over the appropriate residue field for special fibers.".
- Arithmetic_surface wikiPageID "31776898".
- Arithmetic_surface wikiPageRevisionID "602427007".
- Arithmetic_surface hasPhotoCollection Arithmetic_surface.
- Arithmetic_surface subject Category:Articles_created_via_the_Article_Wizard.
- Arithmetic_surface subject Category:Diophantine_geometry.
- Arithmetic_surface subject Category:Surfaces.
- Arithmetic_surface type Artifact100021939.
- Arithmetic_surface type Object100002684.
- Arithmetic_surface type PhysicalEntity100001930.
- Arithmetic_surface type Surface104362025.
- Arithmetic_surface type Surfaces.
- Arithmetic_surface type Whole100003553.
- Arithmetic_surface comment "In mathematics, an arithmetic surface over a Dedekind domain R with fraction field is a geometric object having one conventional dimension, and one other dimension provided by the infinitude of the primes. When R is the ring of integers Z, this intuition depends on the prime ideal spectrum Spec(Z) being seen as analogous to a line.".
- Arithmetic_surface label "Arithmetic surface".
- Arithmetic_surface sameAs m.0gvqzp2.
- Arithmetic_surface sameAs Q4791131.
- Arithmetic_surface sameAs Q4791131.
- Arithmetic_surface sameAs Arithmetic_surface.
- Arithmetic_surface wasDerivedFrom Arithmetic_surface?oldid=602427007.
- Arithmetic_surface isPrimaryTopicOf Arithmetic_surface.