Mathematics Colloquia and Seminars

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When working with algebraic groups over local fields in positive characteristic, ordinary linear algebra turns into Frobenius-twisted linear algebra. We introduce the key players in this Frobenius-twisted setting, called isocrystals. To each isocrystal we show how one can associate a Frobenius-twisted characteristic polynomial, which in turn determines a two-dimensional combinatorial object called a Newton polygon. The collection of Newton polygons then naturally induces a stratification on our algebraic group, called the Newton stratification. We will discuss some of the basic properties of the Newton stratification on GL_n. This talk will be completely self-contained and will include lots of concrete examples.