Anurag Kumar

Interests and Activities

• I'm interested in arithmetic geometry, particularly in p-adic geometry and cohomology, and increasingly, its interactions with homotopy theory.
• I participate in the RIT on p-adic geometry, whose current incarnation is as a learning seminar on Fargues-Scholze.
• I participated in the Spring 2026 six-functor formalisms student seminar, organized by Ziyi Huang.

• Compact generation of D_ét(Bun_G; Λ) - p-adic geometry RIT

  Upcoming, on 6/26/26 - Proving the compact generation of D_ét(U; Λ) for a locally closed substack U ⊆ Bun_G, following Fargues-Scholze §V.4.

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• Computing dualizing objects - Six-functor formalisms student seminar

  3/5/26 - Following this paper of Zavyalov, we explain how (under certain assumptions) to identify the dualizing object f^!1 for a cohomologically smooth morphism in a six-functor formalism on adic spaces or schemes.

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• Basics of ∞-categories - Six-functor formalisms student seminar

  2/5/26 - To prepare for our discussion of six-functor formalisms, we explain the motivation for and fundamentals of ∞-categories (following HTT and these excellent notes of A.A. Khan).

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• Drinfeld level structures - MATH 808L (modular forms and elliptic curves) final presentation

  12/15/25 - We explain the notion of A-level structures on moduli problems for elliptic curves, following the first chapter of Katz-Mazur.

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• Lubin-Tate theory and O_XS(1) - p-adic geometry RIT

  11/14/26 - Following Fargues-Scholze, we explain the computation of the global sections of O(1) on the Fargues-Fontaine curve, which is done via the Lubin-Tate formal group of the local field E.

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• Some adic geometry, and perfectoid fields - p-adic geometry RIT

  6/20/25 and 7/11/25 - We first explain two notions of fiber products that produce adic spaces, namely the adic generic fiber and the internal fiber product within adic spaces. We then switch topics and define perfectoid fields, and prove their basic properties.

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• Deligne's approach to geometric class field theory - MATH 621 (Class field theory) final presentation.

  5/9/25 - We outline Deligne's proof of geometric class field theory, i.e. the analogue of class field theory for curves over finite fields.

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