The Strong Künneth Theorem for Topological Periodic Cyclic Homology

Topological periodic cyclic homology (i.e., <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper T"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {T}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Tate fixed points of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T upper H upper H"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">THH</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) has the structure of a strong symmetric monoidal functor of smooth and proper dg categories over a perfect field of finite characteristic.