Girja S Tripathi | Searcharxiv

arXiv2025

Endomorphisms of Equivariant Algebraic $K$-theory

We prove that for the action of a finite constant group scheme, equivariant algebraic $K$-theory is represented by a colimit of Grassmannians in the equivariant motivic homotopy category. Using this result we show that the set of endomorphisms of the equivariant motivic space defined by $K_0(G,-)$ coincides with the set of endomorphisms of infinite Grassmannians in the equivariant motivic homotopy category by explicitly computing the equivariant $K$-theory of Grassmannians.

math.AG↗

arXiv2024

Constructible Witt theory of schemes

We study the constructible Witt theory of étale sheaves of $Λ$-modules on a scheme $X$ for coefficient rings $Λ$ having finite characteristic not equal to 2 and prime to the residue characteristics of the scheme $X$. Our construction is based on the recent advances by Cisinski and Déglise on six-functor formalism for derived categories of étale motives and offers a background for the study of constructible Witt theory as a cohomological invariant for schemes. In the case of smooth complex algebraic varieties and finite coefficient rings, we show that the algebraic constructible Witt theory studied in this paper can be identified with the topological constructible Witt theory.

math.AG↗