Abstract:Abstract We prove new cases of the direct summand conjecture using fundamental theorems in p -adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies ent...Abstract We prove new cases of the direct summand conjecture using fundamental theorems in p -adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies entirely in characteristic p .Read More