arXiv subjects

Alexander Molyakov

Publications and source records attributed to Alexander Molyakov.

2 recordsLinked to original sources

arXiv2023

Le principe de Hasse pour les intersections de deux quadriques dans $\mathbb{P}^7$

We prove the Hasse principle for a smooth proper model of a geometrically integral non-conical intersection of two quadrics in the projective space of dimension 7 over a number field. This result generalizes the result of Heath-Brown who established the statement in the smooth case. Our argument is built upon the ideas of Colliot-Th\'el\`ene and the fibration method for zero-cycles in the form of Harpaz-Wittenberg.

math.AG↗

arXiv2022

On the fields of definition of genus-one covers of $\mathbb{P}^1$

It is known that sometimes a Belyi pair is not defined over its field of moduli. Instead, it is defined over a finite degree extension of its field of moduli, called a field of definition. We show that given a number $m$ there exists a Belyi pair such that the degree of a field of definition over the field of moduli is greater than $m$. As a byproduct, we obtain a counterexample to the local-global principle for Belyi pairs.

math.AG↗