TY  - BOOK
AU  - Mandal,Poulami
TI  - Embedding problems for the ´etale fundamental group of curves
U1  - P874 23
PY  - 2024///
CY  - Bangalore
PB  - Indian Statistical Institute
KW  - Algebra
KW  - Analytic geometrics
KW  - Algebric geometry
N1  - Thesis (Ph.D.)- Indian statistical Institute, 2024; Includes bibliography; Preliminaries -- Motivation and main problems -- Proofs of the main results; Guided by Prof. Manish Kumar
N2  - 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
UR  - http://dspace.isical.ac.in:8080/jspui/handle/10263/7464
ER  -