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We first consider the basic theory of algebraic curves, including the compact Riemann surface, Riemann-Hurwitz formula, Baker-Akhiezer function, three kinds of Abelian differentials, the construction ...
We define an extended Bloch group for an arbitrary field F, and show that this group is naturally isomorphic to Kind 3 (F) if F is a number field. This gives an explicit descript...
Quillen’s higher algebraic K-theory for fields F has been the object of intense study since their introduction in 1972 [26]. The main direction of research has been the construction of “descen...
his is a relative result which asserts that the K-theory spectra of any two algebraically closed fields of a given characteristic are equivalent to each other after completion at a prime not e...
We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
Let A be a not necessarily commutative monoid with zero such that projective A-acts are free. This paper shows that the algebraic K-groups of A can be defined using the +-construction and the Q-constr...
Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic anal...

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