arXiv subjects

N. Naumann

Publications and source records attributed to N. Naumann.

5 recordsLinked to original sources

arXiv2019

Simultaneous Kummer congruences and $\mathbb{E}_\infty$-orientations of KO and tmf

Building on results of M. Ando, M.J. Hopkins and C. Rezk, we show the existence of uncountably many $\mathbb{E}_\infty$-String orientations of real K-theory KO and of topological modular forms tmf, generalizing the $\hat{A}$- (resp. the Witten) genus. Furthermore, the obstruction to lifting an $\mathbb{E}_\infty$-String orientations from KO to tmf is identified with a classical Iwasawa-theoretic condition. The common key to all these results is a precise understanding of the classical Kummer congruences, imposed for all primes simultaneously. This result is of independent arithmetic interest.

math.AT↗

arXiv2009

Brown representability in $\A^1$-homotopy theory

We prove the following result of V. Voevodsky. If $S$ is a finite dimensional noetherian scheme such that $S=\cup_α\Spec(R_α)$ for {\em countable} rings $R_α$, then the stable motivic homotopy category over $S$ satisfies Brown representability.

math.AG↗

arXiv2005

On the Structure of the Weil Restriction of Abelian Varieties

We give a description of endomorphism rings of Weil restrictions of abelian varieties with respect to finite Galois extensions. The results are applied to study the isogeny decomposition of Weil restrictions.

math.AG↗

arXiv2005

Algebraic independence in the Grothendieck ring of varieties

We give sufficient cohomological criteria for the classes of given varieties over a field $k$ to be algebraically independent in the Grothendieck ring of varieties over $k$ and construct some examples.

math.AG↗

arXiv2003

A motivic version of Pellikaan's two variable zeta function

Combining the idea of motivic zeta function, due to Kapranov, and Pellikaan's definition of a two- variable zeta function for curves over finite fields in the present note we introduce a motivic two- variable zeta function for curves over arbitrary fields and prove the generalizations of Pellikaan's results in this context.

math.AG↗