Time：15:00-16:00, Thursday, November 20 2025
Venue：E4-233
Speaker：Yuri Yatagawa, Institute of Science Tokyo
Title：Index formula of partially logarithmic characteristic cycles
Abstract：In this talk, we consider the computation of the Euler characteristic of an l-adic sheaf on a smooth variety in terms of ramification theory. Ramification theory in arithmetic geometry is a study of relations between cohomological invariants of a constructible sheaf and invariants measuring the ramification of the sheaf. Following Deligne's observation for an analogy between the wild ramification of l-adic sheaves in positive characteristic and the irregular singularity of partial differential equations on a complex manifold, we consider a construction of an algebraic cycle for a constructible sheaf on the cotangent bundle which computes the Euler characteristic as the intersection number with the zero section by using ramification theory .We construct an algebraic cycle on the logarithmic cotangent bundle with logarithmic poles along a subdivisor of the boundary for a smooth sheaf on a smooth variety following Kato's construction of the logarithmic characteristic cycle. After that, we give a formula for the Euler characteristic of the sheaf by using the algebraic cycle constructed with the invariants measuring the ramification of the sheaf.
