تقرير
Derived Moduli Spaces of Nonlinear PDEs I: Singular Propagations
| العنوان: | Derived Moduli Spaces of Nonlinear PDEs I: Singular Propagations |
|---|---|
| المؤلفون: | Kryczka, Jacob, Sheshmani, Artan, Yau, Shing-Tung |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Differential Geometry, Primary: 14A20, 14A30, 35A27, 58A15, 58A20, Secondary: 18N65, 53D30 |
| الوصف: | We construct a sheaf theoretic and derived geometric machinery to study nonlinear partial differential equations and their singular supports. We establish a notion of derived microlocalization for solution spaces of non-linear equations and develop a formalism to pose and solve singular non-linear Cauchy problems globally. Using this approach we estimate the domains of propagation for the solutions of non-linear systems. It is achieved by exploiting the fact that one may greatly enrich and simplify the study of derived non-linear PDEs over a space $X$ by studying its derived linearization which is a module over the sheaf of functions on the $S^1$-equivariant derived loop stack $\mathcal{L}X$. Comment: We have split the previous version into three separate articles due to the invaluable comments from the anonymous referee. Accordingly, the title has also been modified to reflect this change. 84 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.05226 |
| رقم الأكسشن: | edsarx.2312.05226 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |