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Графы на поверхностях и кривые над числовыми полями
27 апреля 2022 г. 18:30–20:00, г. Москва, on-line
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On the fields of definition of genus-one covers of P^1
A. Molyakov Independent University of Moscow
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Эта страница: | 116 |
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Аннотация:
I will discuss some of my recent results related to genus one covers of
the projective line over global fields and their fields of definition.
The absolute Galois group acts on the set of equivalence classes of such
covers in a natural way. The fixed field of the stabilizer with respect
to this action is called the field of moduli of a cover and it is
expected to be the minimal filed of definition. Covers without
automorphisms as well as regular covers are known to be defined over the
field of moduli. However, there are examples of covers (and even of
Belyi pairs) which are not defined over the field of moduli. We will
construct a series of such examples where the degree of a minimal field
of definition over the field of moduli is unbounded. If time permits I
will also discuss counterexamples to the local-global principle for covers.
Язык доклада: английский
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