arXiv subjects

Lorenzo Mantovani

Publications and source records attributed to Lorenzo Mantovani.

5 recordsLinked to original sources

arXiv2026

Equivariant real cycle class map and Witt-sheaf cohomology of classifying spaces

In this paper, we study equivariant real cycle class maps for group actions on real schemes, with a view toward Witt-sheaf characteristic classes. The cycle class maps take values in singular cohomology of the real points of the quotient stack, which are identified with the homotopy fixed-points of complex conjugation on the complex points. This provides a strong relation between Witt-sheaf cohomology of the geometric classifying space of a real algebraic group and the singular cohomology of the classifying spaces of its strong real forms, which we discuss in a number of examples. As a sample application, we compute the number of Witt-sheaf cohomological invariants of spin groups over the reals.

math.AT↗

arXiv2023

Equivariant Chow-Witt groups and moduli stacks of elliptic curves

We introduce equivariant Chow-Witt groups in order to define Chow-Witt groups of quotient stacks. We compute the Chow-Witt ring of the moduli stack of stable (resp. smooth) elliptic curves, providing a geometric interpretation of the new generators. Along the way, we also determine the Chow-Witt ring of the classifying stack of $μ_{2n}$.

math.AG↗

arXiv2023

Experience in Engineering Complex Systems: Active Preference Learning with Multiple Outcomes and Certainty Levels

Black-box optimization refers to the optimization problem whose objective function and/or constraint sets are either unknown, inaccessible, or non-existent. In many applications, especially with the involvement of humans, the only way to access the optimization problem is through performing physical experiments with the available outcomes being the preference of one candidate with respect to one or many others. Accordingly, the algorithm so-called Active Preference Learning has been developed to exploit this specific information in constructing a surrogate function based on standard radial basis functions, and then forming an easy-to-solve acquisition function which repetitively suggests new decision vectors to search for the optimal solution. Based on this idea, our approach aims to extend the algorithm in such a way that can exploit further information effectively, which can be obtained in reality such as: 5-point Likert type scale for the outcomes of the preference query (i.e., the preference can be described in not only "this is better than that" but also "this is much better than that" level), or multiple outcomes for a single preference query with possible additive information on how certain the outcomes are. The validation of the proposed algorithm is done through some standard benchmark functions, showing a promising improvement with respect to the state-of-the-art algorithm.

cs.LG↗

arXiv2021

Localizations and completions of stable $\infty$-categories

We extend some classical results of Bousfield on homology localizations and nilpotent completions to a presentably symmetric monoidal stable $\infty$-category $\mathscr{M}$ admitting a multiplicative left-complete $t$-structure. If $E$ is a homotopy commutative algebra in $\mathscr{M}$ we show that $E$-nilpotent completion, $E$-localization, and a suitable formal completion agree on bounded below objects when $E$ satisfies some reasonable conditions.

math.CT↗

arXiv2018

Localizations and completions in motivic homotopy theory

Let $K$ be a perfect field and let $E$ be a homotopy commutative ring spectrum in the Morel-Voevodsky stable motivic homotopy category $\mathcal{SH}(K)$. In this work we investigate the relation between the $E$-homology localization and $E$-nilpotent completion of a spectrum X. Under reasonable assumptions on $E$ and $X$ we show that these two operations coincide and can be expressed in terms of formal completions or localizations in the usual sense of commutative algebra. We deduce convergence criteria for the $E$-based motivic Adams-Novikov spectral sequence.

math.AG↗