Mehmet Yeşil, The University of Sheffield.
Date: 12th of December, 2018, Thursday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: Let R be a commutative Noetherian ring of prime characteristic p, M be an R-module and e be a positive integer. Let f:R→R be the Frobenius homomorphism given by f(r)=r^p for all r in R whose e-th iteration is denoted by f^{e}. An e-th Cartier map on M is an additive map C:M→M such that rC(m)=C(r^{p^{e}}m) for all r in R and m in M. An R-module is called a Cartier module if it is equipped with a Cartier map. In the case that the Frobenius homomorphism is finite and M is a finitely generated R-module equipped with a surjective Cartier map, it is proved by M. Blickle and G. Böckle in [1] that the set of annihilators of Cartier quotients of M is a finite set of radical ideals consisting of intersections of the finitely many primes in it. In these talks, I will consider the case that R is a finite dimensional polynomial ring over a field of prime characteristic p, and I take a computational view of this finiteness result and drop the finiteness condition on the Frobenius homomorphism to give an alternative proof to the result.
References:
[1] M. Blickle and G. Böckle. Cartier modules: finiteness results.