Embedding problems for the ´etale fundamental group of curves/ Poulami Mandal
Material type:
TextPublication details: Bangalore: Indian Statistical Institute, 2024Description: vii, 63 pagesSubject(s): DDC classification: - 23 516.35 P874
- Guided by Prof. Manish Kumar
| Item type | Current library | Call number | Status | Notes | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|---|
| THESIS | ISI Library, Kolkata | 516.35 P874 (Browse shelf(Opens below)) | Available | E-Thesis | TH603 |
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| 516.35 P481 Motivic aspects of hodge theory / | 516.35 P768 Abelian varieties, theta functions and the fourier transform | 516.35 P863 Lectures on vector bundles | 516.35 P874 Embedding problems for the ´etale fundamental group of curves/ | 516.35 P898 Algebraic cycles, sheaves, shtukas, and moduli | 516.35 P926 Join geometries | 516.35 P988 Emerging applications of algebraic geometry |
Thesis (Ph.D.)- Indian statistical Institute, 2024
Includes bibliography
Preliminaries -- Motivation and main problems -- Proofs of the main results
Guided by Prof. Manish Kumar
Let X be a smooth projective curve over an algebraically closed field k of char- acteristic p > 0, S be a finite subset of closed points in X. Given an embedding problem (β : Γ ↠ G, α : π´et 1 (X \S) ↠ G) for the ´etale fundamental group π´et 1 (X \S), where H = ker(β) is prime-to-p, we discuss when an H-cover W → V of the G- cover V → X corresponding to α is a proper solution. When H is abelian and G is a p-group, some necessary and sufficient conditions for solving the embedding prob- lems are given in terms of the action of G on a certain generalization of Pic0(V )[m], the m-torsion of the Picard group. When a solution exists, we discuss the problem of finding the number of (non-equivalent) solutions and the minimum of genera of the covers corresponding to proper solutions for the given embedding problem.
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