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Super Title Title 2018 KAIST 세미나 Ramification theory and Formal orbifolds Manish Kumar  (  Indian Statistical Institute, Bangalore  ) 2018-06-01 KAIST KAIST Formal orbifolds are normal varieties $X$ over perfect fields with a branch data $P$ which encodes compatible system of finite Galois extensions of function fields of formal neighbourhoods of points of $X$. I will introduce these objects and demonstrate how these objects can be used to study (wild) ramification theory in an organised way. In particular I will define etale site, fundamental group, etc. of formal orbifolds. I will discuss a reasonable formulation of Lefschetz theorem for fundamental group of quasi-projective varieties over fields of positive characteristic in the language of formal orbifolds. Time permitting some partial results in this direction will also be stated.

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