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Results tagged with moduli-spaces
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user 1384
Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.
32
votes
Accepted
Why is one interested in the mod p reduction of modular curves and Shimura varieties?
The Eichler-Shimura relation doesn't just prove the Hasse-Weil conjecture for modular curves. It e.g. attaches Galois representations to modular forms of weight 2. More delicate arguments (using etale …
- 41.4k
8
votes
Proving that a map is a morphism
You have an answer to the 'example' version of your question already, but let me offer an answer to the "actual" question: if one is faced with two schemes $A$ and $B$, and for each $a\in A$ you have …
- 41.4k
5
votes
When is a coarse moduli space also a fine moduli space?
IIRC there's an example due to Gabber in the book by Katz and Mazur of a representable moduli problem where objects have automorphisms (I forget the trick---perhaps he rigged it so that every object h …
- 41.4k