اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCobordism-framed correspondences and the Milnor K-theory
99
0
0.0
(
0
)
تأليف
Aleksei Tsybyshev
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this work, we compute the $0$th cohomology group of a complex of groups of cobordism-framed correspondences, and prove the isomorphism to Milnor $K$-groups. An analogous result for common framed correspondences has been proved by A. Neshitov in his paper Framed correspondences and the Milnor---Witt $K$-theory. Neshitovs result is, at the same time, a computation of the homotopy groups $pi_{i,i}(S^0)(Spec(k)).$ This work could be used in the future as basis for computing homotopy groups $pi_{i,i}(MGL_{bullet})(Spec(k))$ of the spectrum $MGL_{bullet}.$
قيم البحث
اقرأ أيضاً
We introduce a notion of Milnor square of stable $infty$-categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra. We apply this to prove Milnor excision and proper excision theorems in the
K-theory of algebraic stacks with affine diagonal and nice stabilizers. This yields a generalization of Weibels conjecture on the vanishing of negative K-groups for this class of stacks.
We show that the motivic spectrum representing algebraic $K$-theory is a localization of the suspension spectrum of $mathbb{P}^infty$, and similarly that the motivic spectrum representing periodic algebraic cobordism is a localization of the suspensi
on spectrum of $BGL$. In particular, working over $mathbb{C}$ and passing to spaces of $mathbb{C}$-valued points, we obtain new proofs of the topologic
We study a categorical construction called the cobordism category, which associates to each Waldhausen category a simplicial category of cospans. We prove that this construction is homotopy equivalent to Waldhausens $S_{bullet}$-construction and ther
efore it defines a model for Waldhausen $K$-theory. As an example, we discuss this model for $A$-theory and show that the cobordism category of homotopy finite spaces has the homotopy type of Waldhausens $A(*)$. We also review the canonical map from the cobordism category of manifolds to $A$-theory from this viewpoint.
Fix a symbol $underline{a}$ in the mod-$ell$ Milnor $K$-theory of a field $k$, and a norm variety $X$ for $underline{a}$. We show that the ideal generated by $underline{a}$ is the kernel of the $K$-theory map induced by $ksubset k(X)$ and give genera
tors for the annihilator of the ideal. When $ell=2$, this was done by Orlov, Vishik and Voevodsky.
Thomasons {e}tale descent theorem for Bott periodic algebraic $K$-theory cite{aktec} is generalized to any $MGL$ module over a regular Noetherian scheme of finite dimension. Over arbitrary Noetherian schemes of finite dimension, this generalizes the
analog of Thomasons theorem for Weibels homotopy $K$-theory. This is achieved by amplifying the effects from the case of motivic cohomology, using the slice spectral sequence in the case of the universal example of algebraic cobordism. We also obtain integr
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
