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arXiv · 2409.20504

Moduli, Deformations and Algebraic K-Theory of Graded PI-Algebras

Lucio Centrone·Maurício Corrêa
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Abstract

Over a field of characteristic zero, for a finite grading group and a finitely generated graded $T$-ideal, we construct relatively free sheaves and finite-rank quotient stacks of algebra laws with prescribed identities. Their tangent complexes are PI-restricted Hochschild complexes, and the second variations of the identities give explicit lifting obstructions. The first-order deformation groupoid carries a natural relative algebraic K-theory functor; for its square-zero extensions, the relative Chern character identifies rational relative K-theory with negative cyclic homology. Additional identities determine closed PI-strata and localisation fibre sequences in K-theory with Azumaya coefficients. On the Azumaya substack, the degree annihilates the Brauer class, and Morita transport yields a base-change-compatible K-theory of PI-Azumaya families together with a K-theoretic monodromy equivalence.

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Lucio Centrone, Maurício Corrêa. 2024-09-30. Moduli, Deformations and Algebraic K-Theory of Graded PI-Algebras. https://arxiv.org/abs/2409.20504

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