# Factorization of skew polynomials over k((u))

@inproceedings{Borgne2022FactorizationOS, title={Factorization of skew polynomials over k((u))}, author={J{\'e}r{\'e}my Le Borgne}, year={2022} }

Let k be a perfect ﬁeld of characteristic p > 0 , and let K = k (( u )) be the ﬁeld of Laurent series over K . We study the skew polynomial ring K [ T, φ ] , where φ is an endomorphism of K that extends a Frobenius endomorphism of k . We give a description of the irreducible skew polynomials, develop an analogue of the theory of the Newton polygon in this context, and classify the similarity classes of irreducible elements.

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