Dipartimento di Matematica, Sala Seminari.<\/p>\n
Let d be a finite tuple of commuting derivations on a field K.<\/p>\n
A classical result allows us to associate a numerical polynomial to d (the Kolchin polynomial), measuring the “growth rate” of d. A multi-variate version of the same polynomial is also known.<\/p>\n
We show that we can abstract from the setting of fields with derivations, and consider instead a matroid with a tuple d of commuting (quasi)-endomorphisms. In this setting too there exists a (multi-variate) Kolchin polynomial measuring the growth rate of d.<\/p>\n
We can then consider the situation of an o-minimal structure K with a generic tuple d of commuting compatible derivations, and use the corresponding Kolchin polynomial to give a bound to the thorn rank of (K,d).<\/p>\n
<\/p>\n
Joint work with E. Kaplan.<\/p>\n<\/div>\n<\/div>\n<\/div>\n
Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" Let d be a finite tuple of commuting derivations on a field K. A classical result allows us to associate a numerical polynomial to d (the Kolchin polynomial), measuring the “growth rate” of d.\u00a0 A multi-variate version of the same polynomial is also…<\/p>\n