SHEAVES: FROM LERAY TO GROTHENDIECK AND SATO by
نویسندگان
چکیده
— We show how the ideas of Leray (sheaf theory), Grothendieck (derived categories) and Sato (microlocal analysis) lead to the microlocal theory of sheaves which allows one to reduce many problems of linear partial differential equations to problems of microlocal geometry. Moreover, sheaves on Grothendieck topologies are a natural tool to treat growth conditions which appear in Analysis. Résumé (Faisceaux: de Leray à Grothendieck et Sato). — Nous montrons comment les idées de Leray (théorie des faisceaux) Grothendieck (catégories dérivées) et Sato (analyse microlocale) conduisent à la théorie microlocale des faisceaux qui permet de réduire de nombreux problèmes d’équations aux dérivées partielles linéaires à des problèmes de géométrie microlocale. Les faisceaux sur les topologies de Grothendieck sont de plus un outil naturel pour traiter les conditions de croissance qui apparaissent en Analyse.
منابع مشابه
Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics
In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-RochHirzebruch formula for an arbitrary differential operator. Instead of the Grothendieck-Sato isomorphism, we use the Topological Quantum Mechanics (more or less equivalent to the well-known constructions with the Massey operations from [KS], [P], [Me]). The statement that the Massey op...
متن کاملAlgebraic Analysis Applied to the Theory of Linear Dynamical Systems
The expression ”Algebraic Analysis” was coined by Mikio Sato. It consists of using algebraic notions to solve analytic problem. The origin of Algebraic Analysis is Algebraic Geometry as was developed by Alexander Grothendieck and his school. Mimicking the introduction of Grothendieck’s EGA (changing only a few words) one obtains a good definition of the modern theory of linear systems, as devel...
متن کاملMikio Sato, a Visionary of Mathematics, Volume 54, Number 2
Like singularities in mathematics and physics, ideas propagate, and the speed of propagation depends highly on the energy put into promoting them. Mikio Sato did not spend a great deal of time or energy popularizing his ideas. We can hope that his receipt of the 2002/2003 Wolf Prize 1 will help make better known his deep work, which is perhaps too original to be immediately accepted. Sato does ...
متن کاملRecent trends in Algebraic Analysis
I Francesco Baldassarri (Università di Padova) Title: Non-archimedean analysis of irregular singularities Abstract: Let X be a smooth algebraic surface over the complex field C, and Z be a divisor with normal crossings in X. Sabbah’s conjecture on the existence of a good formal structure for an integrable connection on X with poles along Z, has been proved independently by Kiran Kedlaya and Tak...
متن کاملCusps and D-modules
We study interactions between the categories of D-modules on smooth and singular varieties. For a large class of singular varieties Y , we use an extension of the Grothendieck–Sato formula to show that DY -modules are equivalent to stratifications on Y , and as a consequence are unaffected by a class of homeomorphisms, the cuspidal quotients. In particular, when Y has a smooth bijective normali...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004