A generalization of Grothendieck's Extension Panach\'ees
Rakesh Pawar
TL;DR
This paper generalizes the classical extension problem for exact sequences, providing a comprehensive criterion for existence and uniqueness of solutions, thereby extending foundational work in algebraic geometry.
Contribution
It introduces a broad generalization of the extension problem and establishes necessary and sufficient conditions for solutions to exist and be unique.
Findings
Derived a criterion for the existence of solutions
Established conditions for the uniqueness of solutions
Extended classical extension theory in algebraic geometry
Abstract
We formulate a generalization of the extension problem for exact sequences which was considered in [SGA VII] and give a necessary and sufficient criterion for the solution to exist. We also remark on the criterion under which such a solution is unique, if it exists.
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A generalization of Grothendieck’s Extension Panachées
Rakesh R. Pawar
Abstract
We formulate a generalization of the extension problem for exact sequences which was considered in [SGA7] and give a necessary and sufficient criterion for the solution to exist. We also remark on the criterion under which such a solution is unique, if it exists.