arXiv subjects

Serge Yagunov

Publications and source records attributed to Serge Yagunov.

4 recordsLinked to original sources

arXiv2025

Unordered resolutions and homological stability for linear groups

In this paper, we develop a modified proof strategy for homological stability of linear groups, with the general linear groups serving as a primary example. Our arguments are more direct than those in the classical works of Quillen and Suslin--Nesterenko, although they apply only with localized coefficients. The localization at (n-1)! that arises in our approach appears to be closely related to several conjectures of Mirzaii as well as to Suslin's injectivity conjecture.

math.KT↗

arXiv2023

Grothendieck--Witt Groups of Henselian Valuation Rings

We show that functors like algebraic $K$-theory (such as unitary or symplectic $K$-functors), as well as the higher Grothendieck--Witt groups, possess the local constancy condition for Henselian valuation rings. Namely, taken with finite coefficients, these functors send canonical residue maps into isomorphisms. This statement holds in cases of both equal and mixed characteristics. The proof is based on a slight modification of Suslin's methods. In particular, we use his notion of universal homotopy.

math.KT↗

arXiv2008

Duality Theorem for Motives

Using Dold--Puppe category approach to the duality in topology, we prove general duality theorem for the category of motives. As one of the applications of this general result we obtain, in particular, a generalization of Friedlander--Voevodsky's duality to the case of arbitrary base field characteristic.

math.AG↗

arXiv2005

T-spectra and Poincaré Duality

Frank Adams introduced the notion of a complex oriented cohomology theory represented by a commutative ring-spectrum and proved the Poincaré Duality theorem for this general case. In the current paper we consider oriented cohomology theories on algebraic varieties represented by multiplicative symmetric $T$-spectra and prove the Duality theorem, which mimics the result of Adams. This result is held, in particular, for Motivic Cohomology and Algebraic Cobordism of Voevodsky.

math.AG↗