We recall the construction of moduli of abelian schemes. The theory of moduli varieties of abelian varieties has been studied mainly by Shimura and Mumford in the years 1950s to 1960s. Shimura proved the existence of the moduli varieties over a canonically determined number field relative to a given endomorphism ring, a level N-structure and a polarization in the late 1950s to the early 1960s. This gives a modulus over the integer ring of the field with a sufficiently large number of primes inverted.
KeywordsIrreducible Component Abelian Variety Hilbert Scheme Projective Scheme Ample Line Bundle
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