In number theory, a Parshin chain is a higher-dimensional analogue of a place of an algebraic number field. They were introduced by in order to define an analogue of the idele class group for 2-dimensional schemes. A Parshin chain of dimension s on a scheme is a finite sequence of points p0, p1, ..., ps such that pi has dimension i and each point is contained in the closure of the next one. (Wikipedia).
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Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
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Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
Christophe Soulé - 3/4 On the Arakelov theory of arithmetic
Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
Christophe Soulé - 4/4 On the Arakelov theory of arithmetic
Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
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