Geodesic
Idempotents in the endomorphism ring of an ideal in a $p$-extension of a complete discrete valuation field with residue field of characteristic $p$ as a Galois module
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 6, Tome 265 (1999), pp. 22-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study the question when there exist non-trivial idempotents in the endomorphism ring of an ideal in a $p$-extension of a complete discrete valuation field with residue field of finite characteristic $p>2$ as a Galois module. We prove that there are no non-trivial central idempotents for a non-abelian totally widely ramified extension. 
@article{ZNSL_1999_265_a2,
     author = {M. V. Bondarko},
     title = {Idempotents in the endomorphism ring of an ideal in a $p$-extension of a complete discrete valuation field with residue field of characteristic~$p$ as a {Galois} module},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {22--28},
     year = {1999},
     volume = {265},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_265_a2/}
}
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M. V. Bondarko. Idempotents in the endomorphism ring of an ideal in a $p$-extension of a complete discrete valuation field with residue field of characteristic $p$ as a Galois module. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 6, Tome 265 (1999), pp. 22-28. http://geodesic.mathdoc.fr/item/ZNSL_1999_265_a2/