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Session S07 - Differential operators in algebraic geometry and commutative algebra

Friday, July 16, 14:30 ~ 15:00 UTC-3

Valuative aspects of differential algebraic geometry

Cristhian Garay López

Center for Research in Mathematics (CIMAT), México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Broadly speaking, the key ingredient for tropicalization is a generalized non-Archimedean absolute value; that is, is a function defined on a commutative ring with unit that satisfies properties analogous to those of a non-Archimedean absolute value (i.e., Krull valuation), but for which we allow the target to be a commutative idempotent semiring.

In this talk we will introduce non-Krull absolute values for rings of multivariate formal power series (and their fields of fractions) which are defined in terms of Newton polyhedra and polytopes associated to their supports in $\mathbb{N}^m$. We show how to use them to study systems of classical partial algebraic differential equations from a valuative (tropical) point of view.

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