Ramification in arithmetic geometry

研究了局部域的绝对伽罗华群的分支群滤过的分次商的结构。在此基础上，定义了具有正特征的局部域的绝对伽罗华群的L表示的局部傅立叶变换的局部傅立叶变换作为诱导表示，对局部域上任意可构造域上的任意可构造群，定义了Swan类，证明了相对形式的Riemann-Roch型公式。我发表了一篇论文，建立了在p-进Hodge理论意义下与素除p的局部朗兰兹对应的相容。

I studied the structure of graded quotients of the filtration by ramification groups of the absolute Galois group of a local field. Using this, I defined the characteristic variety of an l-adic sheaf under some condition and computed the characteristic class as the intersection product with the 0-section.For an arbitrary constructible sheaf on a variety over a local field, I defined the Swan class and proved a formula of Riemann-Roch type formula in a relative version.I computed explicitly as an induced representation the local Fourier transform of an l-adic representation of the absolute Galois group of a local field of positive characteristic, under a certain assumption.For the p-adic Galois representation associated to a Hilbert modular form, I published a paper establishing the compatibility with the local Langlands correspondence at a prime dividing p in the sense of p-adic Hodge theory