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Yuri Yatagawa

Publications and source records attributed to Yuri Yatagawa.

5 recordsLinked to original sources
arXiv2022

Singular support and Characteristic cycle of a rank one sheaf in codimension two

We compute the singular support and the characteristic cycle of a rank 1 sheaf on a smooth variety in codimension 2 using ramification theory, when the ramification of the sheaf is clean. We develop a general theory, called the partially logarithmic ramification theory, and define an algebraic cycle on a logarithmic cotangent bundle with partial logarithmic poles along the boundary. We prove that the inverse image of the support of the cycle and the pull-back of the cycle to the cotangent bundle are equal to the singular support and the characteristic cycle, respectively, outside a closed subset of the variety of codimension greater than 2 under a mild assumption.

math.AG↗
arXiv2017

Characteristic cycle of a rank one sheaf and ramification theory

We compute the characteristic cycle of a rank one sheaf on a smooth surface over a perfect field of positive characteristic. We construct a canonical lifting on the cotangent bundle of Kato's logarithmic characteristic cycle using ramification theory and prove the equality of the characteristic cycle and the canonical lifting. As corollaries, we obtain a computation of the singular support in terms of ramification theory.

math.AG↗
arXiv2016

Having the same wild ramification is preserved by the direct image

We introduce the notion that two elements of Grothendieck groups of constructible sheaves on a separated scheme over an excellent henselian discrete valuation ring have the same wild ramification. We prove that this condition is preserved by four of Grothendieck's six operations except the derived tensor product and the derived hom.

math.AG↗
arXiv2016

Equality of two non-logarithmic ramification filtrations of abelianized Galois group in positive characteristic

We prove the equality of two non-logarithmic ramification filtrations defined by Matsuda and Abbes-Saito for the abelianized absolute Galois group of a complete discrete valuation field in positive characteristic. We also compute the refined Swan conductor and the characteristic form of a character of the fundamental group of a smooth separated scheme over a perfect field of positive characteristic by using sheaves of Witt vectors.

math.NT↗