Good formal structure for meromorphic flat connections on smooth projective surfaces
نویسنده
چکیده
We prove the algebraic version of a conjecture of C. Sabbah on the existence of the good formal structure for meromorphic flat connections on surfaces after some blow up.
منابع مشابه
Good formal structures for flat meromorphic connections, I: Surfaces
We prove existence of good formal structures for flat meromorphic connections on surfaces after suitable blowing up; this verifies a conjecture of Sabbah, and extends a result of Mochizuki for algebraic connections. Our proof uses a numerical criterion, in terms of spectral behavior of differential operators, under which one can obtain a decomposition of a formal flat connection in arbitrary di...
متن کاملGood formal structures for flat meromorphic connections, II: Higher-dimensional varieties
Given a formal flat meromorphic connection over an algebraic variety over a field of characteristic zero, or a complex analytic variety, we prove existence of good formal structures and a good Deligne-Malgrange lattice after a canonically determined blowing up. This extends our prior result for surfaces; it also reproduces a result of Mochizuki by restricting to algebraic connections. As in our...
متن کاملGood Formal Structures for Flat Meromorphic Connections, Ii: Excellent Schemes
The Hukuhara-Levelt-Turrittin decomposition theorem gives a classification of differential modules over the field C((z)) of formal Laurent series resembling the decomposition of a finite-dimensional vector space equipped with a linear endomorphism into generalized eigenspaces. It implies that after adjoining a suitable root of z, one can express any differential module as a successive extension...
متن کاملGood formal structures for flat meromorphic connections, III: Towards functorial modifications
Given a formal flat meromorphic connection over an excellent scheme over a field of characteristic zero, we proved existence of good formal structures and a good DeligneMalgrange lattice after suitably blowing up. For the corresponding situation over a complex analytic space, one immediately obtains the existence of suitable blowups locally, but it is not clear that these blowups can be glued t...
متن کاملOn Abelian Families and Holomorphic Normal Projective Connections
1.) Pm(C), 2.) smooth abelian families, 3.) manifolds with universal covering Bm(C). Here Bm(C) denotes the ball in C , the non compact dual of Pm(C) in the sense of hermitian symmetric spaces. The second point inlcudes the flat case of an abelian manifold. Any compact Riemann surface admits a holomorphic normal projective connection, this is the famous uniformization theorem. Kobayashi and Och...
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 2008