Alladi Ramakrishnan Hall

Algebraic K-Groups of Varieties over Finite and Local Fields

Jitendra Rathore

University of California, Santa Barbara

In this talk, we will study algebraic K-groups of varieties over finite and local fields. The algebraic K-groups of a variety $X$, denoted $K_n(X)$, are important invariants that encode arithmetic and geometric information about X. We will begin by recalling the definitions and basic properties of these groups, and then present some known results describing their structure. In the latter part of the talk, we will present new results on these groups for algebraic varieties over finite and local fields. This is part of ongoing joint work with Rahul Gupta and Amalendu Krishna.