分野別セミナー

The usual language of algebraic geometry is not appropriate for Arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace rings by the collection of “vectors” or by bi-operads and another based on “matrices” or props. Once one understands the delicate commutativity condition one can proceed following Grothendieck footsteps exactly. The square matrices , when viewed up to conjugation, give us new commutative rings with Frobenius endomorphisms.