Seminario Ruso
Miércoles 24 de noviembre de 2021
10:30hrs
Palapa Nueva
Imparte(n)
Responsable(s):
By a degeneration, we mean a process that transforms a geometric object $X/F$ defined over a field $F$ into a simpler object that retains many of the relevant properties of $X$.
Formally, any degeneration is realized by an integral model for $X$; that is, a flat scheme $X’/R$ defined over some integral domain $R$ whose generic fiber is the original object $X$.
In this talk, we endow the field $F=K((t_1,\ldots,t_m))$ of quotients of multivariate formal power series with a generalized non-Archimedean absolute value $|\cdot|$, and we establish the existence of integral models over the ring of integers $R=\{|x|\leq 1\}$ for solutions $X$ of systems of algebraic partial differential equations with coefficients on $F$. We also concretely describe the specialization map of a model $X’/R$ to the maximal ideals of $R$, which are encoded in terms of monomial orderings.
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