[Turkmath:7341] FGC-HRI-IPM Sayılar Teorisi Semineri::James Borger:: Aralık 03, 2025 saat 12:00

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Sayın Matematikçiler,

Bu Çarşamba (3 Aralık 2025) öğleyin saat 12:00'da FGC-HRI-IPM Sayılar 
Teorisi Seminer Dizisinde James Borger (ANU) konuşacaktır. Detayları 
aşağıda verilmiştir...

İyi çalışmalar,
İlhan İkeda

>  FGC-HRI-IPM Number Theory Seminars

>  Date: December 3, 2025 at 12:00 pm

>  Speaker: James Borger (Australian National University)
>  Title: Scheme theory over semirings
> 
> Abstract: Usual scheme theory can be viewed as the syntactic theory of
> polynomial equations with coefficients in a ring, most importantly the
> ring of integers. But none of its most fundamental ingredients, such
> as faithfully flat descent, require subtraction. So we can set up a
> scheme theory over semirings (``rings but possibly without additive
> inverses’’, such as the non-negative integers or reals), thus
> bringing positivity in to the foundations of scheme theory. It is then
> reasonable to view non-negativity as integrality at the infinite
> place, the Boolean semiring as the residue field there, and the
> non-negative reals as the completion.
> 
> In this talk, I'll discuss some recent developments in module theory
> over semirings. While the classical definitions of ``vector bundle''
> are not all equivalent over semirings, the classical definitions of
> ``line bundle'' are all equivalent, which allows us to define Picard
> groups and Picard stacks. The narrow class group of a number field can
> be recovered as the reflexive class group of the semiring of its
> totally nonnegative integers, i.e. the arithmetic compactification of
> the spectrum of the ring of integers. This gives a scheme-theoretic
> definition of the narrow class group, as was done for the ordinary
> class group a long time ago.
> 
> This is based mostly on arXiv:2405.18645, which is joint work with
> Jaiung Jun, and also on forthcoming paper with Johan de Jong and Ivan
> Zelich.
> 
> Zoom link details:
> Online Link: https://kocun.zoom.us/j/99715471656
> Toplantı Şifresi: Meeting ID: 997 1547 1656 passcode: 848084
> 
> TMD Seminerleri web sayfası: 
> https://www.turkmath.org/beta/seminer.php?id_seminer=4074