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Explore finiteness questions for étale coverings with bounded wild ramification at the boundary in this 58-minute conference talk by Vasudevan Srinivas at ICBS2024. Delve into the study of étale coverings f:Y→X of varieties over algebraically closed fields in positive characteristic, with specific focus on boundary ramification in non-proper cases. Gain insights into recent collaborative work with Hélène Esnault and others, examining key developments in this area over the past few years. Discover open problems and ongoing research related to this theme, enhancing your understanding of algebraic geometry and number theory concepts.